Tuesday 25 September 2012
Lecture 1 post hoc notes - Legal Aspects of Corporate Finance
Lecture 1: Legal Aspects of Corporate Finance
Guest instructors: Professor Edmond Curtin and PhD Candidate Rezarte Vukatana
I walked in a few minutes late with a bundle of papers and just started talking about THEORY as if it were the most natural thing in the world. I told them about a Russian table tennis star whose training regime included 6 hours of chalk and blackboard theory everyday. But the main point came from Hohfeld's definition of theory: "A theory is not even a theory unless it can be used by practitioners in their practice." I don't think I introduced myself but I did introduce Edmond and later Rezi. I mentioned a few themes:
(1) WEAK EQUIVALENCE as the subtle equivalence of thoughts;
(2) the UNITY OF SCIENCE CRITERION as the main ground for adjudicating theories-- a theory should be judged on how it helps us understand the unity of all knowledge of being;
(3) sign, symbol (Edmond mentioned "signifier" pointing to the picture of the green man in the exit sign--everyone turned to look);
(4) HOHFELD the undergrad chemistry student turned professor of Yale Law School who in early 20th century wrote only 6 articles and invented a periodic table for the law - 4 JURAL OPPOSITES and 4 JURAL CORRELATIVES with enormous theoretical effects;
(5) CORBIN and WILLISTON who wrote encyclopediac tomes on contracts law, and how Corbin (a Hohfeldian student) took just one jural correlative, rights versus duties, and turned that tiny almost trivial legal distinction into 7 (or was it 9?) volumes of contract law;
(6) And Where are Contracts anyway? shock horror to the civil law students ["on paper", "after the signature" they say] but no, says the common law jurisprudentem--CONTRACTS EXIST IN THE MIND [Edmond]; horror of horrors, is this the pure subjectivism, relativism and thus, total discretionary totalitarianism of the law?;
(7) Why some questions within professional discourse make no sense ("What's north of the north pole, eh?"] and is there a way of understanding that transcends the bounds of discourse? Later, the astute Russian student answering a question about "material information" asked a rhetorical question about the distinguishment of various risks. Then I told a long story about Yuanjia, the Great Wun Chin master, who when cajoled by a Japanese martial artist that there are levels in the artistry of tea, replied, "The tea makes no such distinctions and is thoroughly enjoyed."
Thankfully, Edmond gave us a brief rendition on some of the essential legal principles of DERIVATIVES--how they actually create MORE RISK and MORE ANXIETY, and never less.
Rezi described part of her PhD dissertation research--theory of self-fulfilling prophecy a la Merton (?) and how this can be used to help explain the strange behaviours of very complex nodes of financial system called intermediated securities accounts.
I passed around 3 LLM dissertations for the students' inspection, and gave them a homework assignment.
I filed some prospectuses at LLMCFL2012@gmail.com [if you want the password, you need to contact me] with my notes, and asked the students to write 2,000 words on (1) the risks of the prospectus transaction (either Salvatore Ferragamo or Prada); and (2) determine whether and what parts of the selected prospectus would need to be changed under the Directive 2010/73 Nov 2010. They'll need to review about 600 to 800 pages and email me their work by 12noon Monday. Nice shock therapy.
Tuesday 11 September 2012
Extreme Philosophy: On the Limits of Self-Referential Truth: Why Paradox Has Been Binned By Naive Category Theory
1. Here are two papers of EXTREME PHILOSOPHICAL SIGNIFICANCE:
[1] Lawvere, F. William, "Diagonal arguments and cartesian closed categories with Author Commentary," Lecture Notes in Mathematics, 92 (1969), 134-145, available at:
http://www.tac.mta.ca/tac/reprints/articles/15/tr15.pdf
[2] Yanosky, Noson (2003) "A Universal Approach to Self-Referential Paradoxes, Incompleteness and Fixed Points," available at: http://arxiv.org/pdf/math/0305282v1
2. Unless you've studied a bit of category theory, i.e., read Lawvere and Schanuel (2008, 2nd edition) and Lawvere and Roseburgh (2003), Lawvere [1] will be very obscure even with Lawvere's commentary. But take a look and get a feel. Then, look at Yanosky [2] which explains in a more breezy (but precise) way what the genius Lawvere was up to, and even more cleverly in order to reach a "wider audience", dropped category theory altogether and explains Lawvere's discoveries in easy enough "set and function" language.
3. I realize that category theory is not for everybody (yet) and recently, in the literature, there is a push-back accusing category theory of making "foundational claims" that are unjustified. For example, that the entirety of mathematics can be put on a category theory footing and replace set theory as the fundamental theory which all other theories must bow down to. But I don't think category theory as it is practiced sets out to make any really big claims like these--that would be the job of propogandists. Rather it "solves" some rather apparent fundamental problems by "resolving" the problems into a diagrammatic logic. If you buy the diagrams as BEING DENOTIVE then you might also see how category theory IS linked to Aristotle's great work On Categories. Mac Lane in a footnote joked about how the title "category theory" came from "purloining words from the philosophoers, Aristotle and Kant" [pp. 29-30 of Categories for the Working Mathematician]. He doesn't say anything more about this jokey link. But if you read and understand Aristotle's motive in his Categories, you can see immediately that Aristotle set up foundational problems so they can be resolved. He analysed knowledged into what might be called "said-of" and "thing-in" and asked what are those abstractions that are primary, that is, what are those properties that are extended and therefore, must be. He listed 10 categories [what they are appears arbitrary] and he showed how you can use these primary categories to categorize everything else, that is, that which is not so extended and universal. Now, this mental-conceptual move to abstraction in order to solve a particular problem is a natural function. Lawvere & Schanuel in Conceptual Mathematics explain this movement in terms of isomorphisms: e.g. think of how you can understand what's happening in a film even after walking into the cinema late. In media res, you know Humphrey Bogart is playing a particular character and Audrey Hepburn is playing another character, and when you sort out who's who in the film, suddenly, you can follow the plot in the film with the actors as playing their roles. Similarly, being born in the middle of things, we open our eyes, stretch our arms and legs, and explore the universe, fully confident that we will be able to sort EVERYTHING out. This confidence comes from something pretty powerful within ourselves that enables us to gain knowledge. And the point here is that knowledge isn't at its rock bottom paradoxical. It is in all likelihood isomorphic.
4. Lawvere [1] takes a swipe at the propogandists who have been using some of the great theoretical work of theorists (such as Russell, Cantor, Godel, Tarski) and turned them into very general claims about the nature of paradox at the heart of knowledge. To put this into a general philosophical context, Aristotle's optimism was founded on his discovery of a general scientific method which if simply re-iterated, would eventually uncover all the mysteries of the universe. It was based on observing that which is and translating those into propositions which could be understood. If at the heart of heart of "proposition making" we have paradox, then this whole enterprise is doomed to failure. So, burdened with the prospect of failure, why start the programme of knowledge?
5. The answer by Lawvere [1] and Yanofsky [2] shows why the propogandists of paradox are simply wrong. In Yanofsky's terms, Lawvere's great little paper [1] has been largely ignored by category theorists and philosophers alike because it is written in a forbidding unpopular formalism. Yanofsky translates the results of Lawvere's paper by saying the classical paradoxes of self-referential truth (e.g. Liar's paradox, Russell paradox, Godel's incompleteness and so on) are just instances of overstepping the limitations of a discourse ("discourse" is my term). There must be a way of limiting what a discourse can say about itself. This "problem" comes up in law and finance whenever they try to talk about themselves. I call it the problem of structure. That is, there is no such question in law and finance that says, "What is the structure of law? What is the structure of statements about finance?" There is no call for self-consciousness within laws or financial practice. Rather, the call for such professional consciousness comes from without. But there is a way of understanding such questions about professional discourses from a category theory perspective. And not only do the questions about the structure of law and finance make sense, they actually direct in some fashion a resolution to answers about the structure of law and finance.
For example, one of the things I have been harping on in this blog is that there is a fundamental structure to law and finance in the forms of an individual unit which I have dubbed the "financial contract" and the "great cycle of default invariance." From these structures, we can explain a lot of current practice at the individual-to-individual level of financial transactions on up to historical and contemporary nausea of continuously impending financial catastrophes. It's all a matter of "mapping" and translating apparent limitations within the discourse of law and finance into a notation which allows for mental journeys and conceptual calculations. By the way, one of the virtues of seeing how paradoxes are slain in [1] and [2] is that we can recover a sense of optimism that Aristotle once had in the unity of science. Again, I say, judge the value of a theory by its contribution to the unity of science.
Monday 14 May 2012
On the Unity of Science: Law, Finance and the Philosophy of Category Theory
1. We should measure our progress as a species of knowledge by how well individual disciplines meet the criterion of the unity of science. This criterion was first stated as an almost urgent request by Edward O. Wilson with his concept of consilience.
2. There are so many analogies between one subject and another, the vocabularies (as objects may be different), but the way in which these vocabularies are used (the morphisms) are so similar that they might as well be said to be the same. What do we mean by "same" or better, if we capture the water colourist wash, and call it by its technical name, "weakened equivalence"?
3. Mazur (June 12, 2007) in "When is one thing equal to some other thing," htt://www.math.harvard.edu/%7Emazur/preprints/when_is_one.pdf writes in tribute to one of the founders of category theory, Mac Lane, sets out an approachable essay on the question of the meaning of equivalence. This is the deep point where all our equations and assertions in science sink to. He sets out three approaches of how we have answered this question.
4. The first is the "bureau of standards" where by convention we can point to something in a designated office that is an equivalent exemplar. [Id @ 4-5.] The second is a type of universal quantification as in Frege's definition of cardinality. [Id @ 5.] And the third is a compromise where "we indicate what we do rather than what we say we do when quizzed about our foundations." [Ibid.] I call this third method a promiscuous stitching, using the same needle and thread or glue may be all we need to make appropriate connections between subjects, disciplines and fields of knowledge.
5. In mathematics, you can "package" entire mathematical theories either as (1) formal systems a la the David Hilbert programme or as (2) categories. [Id @6.] On the one hand, the formal systems go all the way back to Euclid and are much admired under the rubric of axiomatization. On the other hand, categories are a relatively recent invention (1945 with a paper by Samuel Eilenberg and Saunders Mac Lane was more an announcement of new technique than a new view of mathematics) and its method of a sparse vocabulary and sketches of arrows betrays its deep goal which is to reveal structure. Mathematicians, like others engaged in doing or performing in their particular discourse, don't really "axiomize" but rather "play games with conviction."
6. Somewhere in "Tool and Object, A History and Philosophy of Category Theory," (2007), Kromer quotes Bill Lawvere (my preferred radical category theorist) for saying something to the effect, "the point is not to achieve maximal abstraction, but an optimal abstraction, a just-right abstraction that works appropriately at the level where it is most needed and used." Of course, I am attributing a certain line of argument to Lawvere which I do not think he would disagree with. Lawvere was motivated to find a theory of physics, to explain how things worked, but his work on the philosophy of category theory takes him on exoduses into Hegel. I believe it is this urge to find "synthesis" with simple tools that motivates him. He has been accused of being both revolutionary and idiosyncratic. Revolutionary for advocating that all of mathematics can be thought of as a category of category theory. And idiosyncratic because for such a great mathematician, he and Schanuel wrote a best selling book entitled, Conceptual Mathematics, A First Introduction to Category Theory (2009 2nd Edition) wherein you don't need any university level mathematics to understand. In fact, I recommend this book to all my law and finance students who are interested in pursuing the application of category theory to the field of law and finance.
7. The main points about the test for the unity of science (consilience) is that the most appropriate method for pursuing a rigorous apprehension of science (i.e., the three approaches stated by Mazur: bureaucratic standard, universal axiomization or balanced compromse (I call "promiscuous stitching") may be something so natural and simple that even our high school students can be engaged in this entreprise.
8. For theories of law and finance, we see that there has been an influence of the latest trend or fashion from other fields that have filtered into the vocabulary of the legal theorist or financial theorist. For example in the last 5 to 10 years, in both fields there is an emphasis at least in the titles to papers on the concept of "complexity" and "behaviours." This is not to say these concepts are red-herrings. From my view, they are just another batch of ideas that come from a few equations. Another example, what would Hart's programme of primary and secondary laws be without the notions of first order and second order logics emanating from the Cambridge logicians in the early part of the 20th century? Not that Hart genuinely meant to implement the same programme, but the inspiration for an orderly resolution of the definition of the meaning of law was certainly intended to take the script from the philosophy department--and these were the ideas pre-Wittengstein. In finance, the initial idea of covariance goes back to Bachelier's PhD dissertation (1905) and then developed as various methods for "curve fitting" against time horizons. Very little work has been done on how the various theories of law and finance might be approached in a unified way. But here the stumbling block may have been the limited view on the number of approaches to reach unification. I do not mean by "unification" a form of axiomatiion or foundational premises evolved and expanded in a universalistic sense that may have endeared Spinoza. Rather we have a very powerful alternative which is a kind of Kantian insight that the intellectual revolution begins with a recognition that
"There are only two possible ways in which synthetic representations and their objects...can meet one another. Either the object (Genenstand) alone must make the representation possible, or the representation alone must make the object possible." [quoted from Mazur supra @ 20.]
9. In law and finance theory, I would (and will) argue that one of the significant leaps in our imagination of how law and finance work together is to recognize the structure of something called "default invariance." This is captured by or very conveniently set out with a category theory approach. Default invariance permeates all financial contracts, and all states of the financial-regulatory-political system.
2. There are so many analogies between one subject and another, the vocabularies (as objects may be different), but the way in which these vocabularies are used (the morphisms) are so similar that they might as well be said to be the same. What do we mean by "same" or better, if we capture the water colourist wash, and call it by its technical name, "weakened equivalence"?
3. Mazur (June 12, 2007) in "When is one thing equal to some other thing," htt://www.math.harvard.edu/%7Emazur/preprints/when_is_one.pdf writes in tribute to one of the founders of category theory, Mac Lane, sets out an approachable essay on the question of the meaning of equivalence. This is the deep point where all our equations and assertions in science sink to. He sets out three approaches of how we have answered this question.
4. The first is the "bureau of standards" where by convention we can point to something in a designated office that is an equivalent exemplar. [Id @ 4-5.] The second is a type of universal quantification as in Frege's definition of cardinality. [Id @ 5.] And the third is a compromise where "we indicate what we do rather than what we say we do when quizzed about our foundations." [Ibid.] I call this third method a promiscuous stitching, using the same needle and thread or glue may be all we need to make appropriate connections between subjects, disciplines and fields of knowledge.
5. In mathematics, you can "package" entire mathematical theories either as (1) formal systems a la the David Hilbert programme or as (2) categories. [Id @6.] On the one hand, the formal systems go all the way back to Euclid and are much admired under the rubric of axiomatization. On the other hand, categories are a relatively recent invention (1945 with a paper by Samuel Eilenberg and Saunders Mac Lane was more an announcement of new technique than a new view of mathematics) and its method of a sparse vocabulary and sketches of arrows betrays its deep goal which is to reveal structure. Mathematicians, like others engaged in doing or performing in their particular discourse, don't really "axiomize" but rather "play games with conviction."
6. Somewhere in "Tool and Object, A History and Philosophy of Category Theory," (2007), Kromer quotes Bill Lawvere (my preferred radical category theorist) for saying something to the effect, "the point is not to achieve maximal abstraction, but an optimal abstraction, a just-right abstraction that works appropriately at the level where it is most needed and used." Of course, I am attributing a certain line of argument to Lawvere which I do not think he would disagree with. Lawvere was motivated to find a theory of physics, to explain how things worked, but his work on the philosophy of category theory takes him on exoduses into Hegel. I believe it is this urge to find "synthesis" with simple tools that motivates him. He has been accused of being both revolutionary and idiosyncratic. Revolutionary for advocating that all of mathematics can be thought of as a category of category theory. And idiosyncratic because for such a great mathematician, he and Schanuel wrote a best selling book entitled, Conceptual Mathematics, A First Introduction to Category Theory (2009 2nd Edition) wherein you don't need any university level mathematics to understand. In fact, I recommend this book to all my law and finance students who are interested in pursuing the application of category theory to the field of law and finance.
7. The main points about the test for the unity of science (consilience) is that the most appropriate method for pursuing a rigorous apprehension of science (i.e., the three approaches stated by Mazur: bureaucratic standard, universal axiomization or balanced compromse (I call "promiscuous stitching") may be something so natural and simple that even our high school students can be engaged in this entreprise.
8. For theories of law and finance, we see that there has been an influence of the latest trend or fashion from other fields that have filtered into the vocabulary of the legal theorist or financial theorist. For example in the last 5 to 10 years, in both fields there is an emphasis at least in the titles to papers on the concept of "complexity" and "behaviours." This is not to say these concepts are red-herrings. From my view, they are just another batch of ideas that come from a few equations. Another example, what would Hart's programme of primary and secondary laws be without the notions of first order and second order logics emanating from the Cambridge logicians in the early part of the 20th century? Not that Hart genuinely meant to implement the same programme, but the inspiration for an orderly resolution of the definition of the meaning of law was certainly intended to take the script from the philosophy department--and these were the ideas pre-Wittengstein. In finance, the initial idea of covariance goes back to Bachelier's PhD dissertation (1905) and then developed as various methods for "curve fitting" against time horizons. Very little work has been done on how the various theories of law and finance might be approached in a unified way. But here the stumbling block may have been the limited view on the number of approaches to reach unification. I do not mean by "unification" a form of axiomatiion or foundational premises evolved and expanded in a universalistic sense that may have endeared Spinoza. Rather we have a very powerful alternative which is a kind of Kantian insight that the intellectual revolution begins with a recognition that
"There are only two possible ways in which synthetic representations and their objects...can meet one another. Either the object (Genenstand) alone must make the representation possible, or the representation alone must make the object possible." [quoted from Mazur supra @ 20.]
9. In law and finance theory, I would (and will) argue that one of the significant leaps in our imagination of how law and finance work together is to recognize the structure of something called "default invariance." This is captured by or very conveniently set out with a category theory approach. Default invariance permeates all financial contracts, and all states of the financial-regulatory-political system.
Friday 13 April 2012
HFT FLASH CRASHES AND REGULATION: AN INCHOATE BIBLIOGRAPHY
( ) Research question: Why is it important to understand the physical limits of financial trading?
( ) Application: possible training course for supervisors and regulators around the world
I shall be adding to this list of references from time to time and reorganising its entirety when appropriate:
( ) IOSCO'S Recommendation for Standard Regulation on HFTs
Regulatory Issues Raised by the Impact of Technological Changes on Market Integrity and Efficiency - Consultative Report
OISU - ISOCO (July 2011)
http://www.iosco.org/library/pubdocs/pdf/IOSCOPD354.pdf
( ) SEC Report on May 6, 2010 Flash Crash (100930)
http://www.sec.gov/news/studies/2010/marketevents-report.pdf
( ) Zerohedge (100623): http://www.zerohedge.com/article/how-hft-quote-stuffing-caused-market-crash-may-6-and-threatens-destroy-entire-market-any-mom
( ) Nanex Analysis of the Flash Crash (100618): http://www.nanex.net/20100506/FlashCrashAnalysis_CompleteText.html
[ ] pay particular attention to "quote stuffing" which Nanex says should be banned: http://www.nanex.net/20100506/FlashCrashAnalysis_Part4-1.html
( ) Nanex Analysis of the SEC's Flash Crash (May 6, 2010) Report of Sept 30, 2010 (120412):
( ) Email exchange on the definition of LIQUIDITY: http://www.nanex.net/aqck/2977.html
( ) Nanex updated analysis on April 11, 2011--check out the 2nd chart especially when Wadell and Clarke whom the SEC has blamed for the Flash Crash and the W&C has accepted such blame, could NOT PHYSICALLY be the one who was involved in the perpetration of the flash crash! http://www.nanex.net/FlashCrashFinal/FlashCrashAnalysis_WR_Update.html
Background Readings:
[ ] http://www.zerohedge.com/article/guest-post-deconstructing-algos-part-1
[ ] http://www.zerohedge.com/article/guest-post-deconstructing-algos-part-2-leveraging-chaos-high-frequency-arbitrage-opportuniti
[ ] http://www.zerohedge.com/article/guest-post-deconstructing-algos-3-quote-stuffing-means-restoring-arbitrageable-latency-or-cq
[ ] http://www.zerohedge.com/news/guest-post-deconstructing-algos-part-4-phase-space-reconstructions-cnty-busted-trades-suggests-
HFT REVIEW White papers, academic and industry reports
ACADEMIC ARTICLES ON POINT
http://www.hftreview.com/pg/main/academic-studies/
INVESTIGATIONS
[ ] SEC Probes Ties to High Speed Traders
http://online.wsj.com/article/SB10001424052702303816504577321864050711038.html
NY TIMES ARTICLES
135 articles on high frequency trading as of April 4, 2012
http://topics.nytimes.com/topics/reference/timestopics/subjects/h/high_frequency_algorithmic_trading/index.html
EUROPEAN REGULATIONS
[ ] MiFID 2 Barnier
http://hft.thomsonreuters.com/2010/09/23/eus-barnier-throws-spotlight-on-dark-pool-trades/
REUTERS THOMSON HFT NEWS
http://hft.thomsonreuters.com/
WHARTON article
http://knowledge.wharton.upenn.edu/article.cfm?articleid=2345
INSTITUTIONAL INVESTOR
10 articles
http://www.iijournals.com/page/HighFrequencyTrading
ACADEMIC PAPERS
[ ] Conflicting Codes and Codings
How Algorithmic Trading Is Reshaping Financial Regulation
Marc Lenglet
Abstract
Contemporary financial markets have recently witnessed a sea change with the ‘algorithmic revolution’, as trading automats are used to ease the execution sequences and reduce market impact. Being constantly monitored, they take an active part in the shaping of markets, and sometimes generate crises when ‘they mess up’ or when they entail situations where traders cannot go backwards. Algorithms are software codes coding practices in an IT significant ‘textual’ device, designed to replicate trading patterns. To be accepted, however, they need to comply with regulatory texts, which are nothing else but codes of conduct coding accepted practices in the markets. In this article, I draw on ethnographic fieldwork in order to open these black boxes, while trying to describe their existence as devices encapsulating several points of views. I address the question of a possible misalignment between those visions, and more specifically try to draw the consequences raised by such discrepancies as regards the future of financial regulation.
algorithmic trading codes of conduct codings financial markets practices regulation
Articles citing this article
Codes and Codings in Crisis: Signification, Performativity and Excess
Theory, Culture & Society November 1, 2011 28: 3-23
AbstractFull Text (PDF)
[ ] Investigating Financial Fraud in High Frequency Trading
Afroditi Katika
University of Manchester
Babis Theodoulidis
University of Manchester - Manchester Business School
David Diaz
University of Manchester - Manchester Business School; Universidad de Chile - Escuela de Economia y Negocios
December 20, 2011
Abstract:
Market monitoring is a very important process to the stock market. It is necessary in order to verify that all trades comply with the existing rules, as well as to detect any act of manipulation. Recently, a new kind of trading has emerged, High Frequency Trading, which allows traders to place and execute orders within milliseconds via a program running in a computer. It is doubtful whether existent market systems are capable of detecting inconsistencies in trades at this speed. This project has attempted to propose a design of a detection engine that could be incorporated to a monitoring framework so as to accommodate High Frequency trades. Understanding the field of stock markets and High Frequency Trading was a crucial part of this project. Since it is such a recent phenomenon with no confirmed cases (to the best of our knowledge) of market manipulation, we attempted to answer whether there are certain conditions that could benefit market manipulators. We used business intelligence techniques to analyse historical data and discover what sort of indications our detection engine should look for. Our results show that there have been violations of regulations that were not blocked in real-time which proves the inefficiency of current market monitoring systems. We also prove that an extreme number of orders within seconds can delay an exchange’s processes and systems. In the end we propose a design that takes those results into consideration.
Keywords: high frequency trading, flash crash, quote stuffing, financial markets, market manipulation, fraud detection, market monitoring, market surveillance
Working Paper Series
Date posted: December 20, 2011
Suggested Citation
Katika, Afroditi, Theodoulidis, Babis and Diaz, David, Investigating Financial Fraud in High Frequency Trading (December 20, 2011). Available at SSRN: http://ssrn.com/abstract=1974911
[ ] On the Dark Side of the Market: Identifying and Analyzing Hidden Order Placements
Nikolaus Hautsch
Humboldt-Universität zu Berlin; CASE - Center for Applied Statistics and Economics; CFS
Ruihong Huang
Humboldt University of Berlin
February 8, 2012
Abstract:
Trading under limited pre-trade transparency becomes increasingly popular on financial markets. We provide first evidence on traders' use of (completely) hidden orders which might be placed even inside of the (displayed) bid-ask spread. Employing TotalView-ITCH data on order messages at NASDAQ, we propose a simple method to conduct statistical inference on the location of hidden depth and to test economic hypotheses. Analyzing a wide cross-section of stocks, we show that market conditions reflected by the (visible) bid-ask spread, (visible) depth, recent price movements and trading signals significantly affect the aggressiveness of 'dark' liquidity supply and thus the 'hidden spread'. Our evidence suggests that traders balance hidden order placements to (i) compete for the provision of (hidden) liquidity and (ii) protect themselves against adverse selection, front-running as well as 'hidden order detection strategies' used by high-frequency traders. Accordingly, our results show that hidden liquidity locations are predictable given the observable state of the market.
Number of Pages in PDF File: 43
Keywords: limit order market, hidden liquidity, high-frequency trading, non-display order, iceberg orders
JEL Classifications: G14, C24, C25, G17
Working Paper Series
Date posted: February 13, 2012
Suggested Citation
Hautsch, Nikolaus and Huang, Ruihong, On the Dark Side of the Market: Identifying and Analyzing Hidden Order Placements (February 8, 2012). Available at SSRN: http://ssrn.com/abstract=2004231 or http://dx.doi.org/10.2139/ssrn.2004231
CASE STUDIES
[ ] BATS Take-down
http://www.zerohedge.com/news/skynet-wars-how-nasdaq-algo-destroyed-bats
[ ] http://www.zerohedge.com/news/presenting-todays-21-least-mini-flash-crashes
[ ] http://www.zerohedge.com/article/fractal-limit-order-buster-latest-market-manipulation-algo-gimmick
[ ] Man Vs Machine: How Each Sees The Stock Market
Submitted by Tyler Durden on 04/03/2012
available at: http://www.zerohedge.com/news/man-vs-machine-how-each-sees-stock-market
[ ] http://www.zerohedge.com/news/fractal-algo-strikes-again-time-impacts-popular-bond-bear-etf-tbt
[ ] http://www.zerohedge.com/news/stop-loss-terminator-algo-reemerges-picks-national-bank-greece-todays-victim
[ ] http://www.zerohedge.com/news/dear-hft-please-explain
[ ] http://www.zerohedge.com/news/step-right-its-hft-whack-mole-time
[ ] http://www.zerohedge.com/news/whack-mole-algo-back
[ ] http://www.zerohedge.com/article/are-hft-algos-taking-aim-dominating-and-manipulating-wonderful-world-etfs-next
[ ] http://www.zerohedge.com/article/visualizing-market-topology-video-real-time-exchange-routing
[ ] http://www.zerohedge.com/news/does-high-frequency-trading-adds-market-liquidity-vote-here
[ ] http://www.zerohedge.com/article/hft-now-business-frontrunning-each-others-regulatory-capture
[ ] http://www.zerohedge.com/article/caught-act-hft-option-algos-observed-frontrunning-todays-pmi-release
[ ] http://www.zerohedge.com/article/some-observations-spy-vwap-and-block-manipulation-fsa-launches-probe-front-running-block-tra
[ ] http://www.zerohedge.com/article/no-its-not-nat-gas-fractal-algo-nanex-discloses-very-ominous-implications-todays-berserk-cru
[ ] http://www.zerohedge.com/article/another-algo-gone-wild
RANDOM QUOTES:
[ ] Guest Post: Deconstructing Algos, Part 4 -Phase Space Reconstructions Of CNTY Busted Trades Suggests High Speed Gang-Bangs In The Market
Submitted by The World Complex Deconstructing Algos, Part 4: Phase Space ... Volatility Submitted by The World ComplexDeconstructing Algos, Part 4: Phase Space Reconstructions ... the algos picked up by Nanex on June 21, 2011 in CNTY using the data appended here . ...
Story - Tyler Durden - 07/31/2011 - 17:43 - 39 comments - 0 attachments
[ ] Guest Post: Deconstructing Algos, Part 2: Leveraging Chaos Into High-Frequency Arbitrage Opportunities
Submitted by The World Complex Deconstructing Algos, Part 2: Leveraging Chaos Into High-Frequency Arbitrage Opportunities The recent elegant explanation for the activities of the HFT algos ... Natural Gas Submitted by The World ComplexDeconstructing Algos, Part 2: Leveraging Chaos ...
[ ] Story - Tyler Durden - 07/01/2011 - 00:21 - 32 comments - 0 attachments
Guest Post: Deconstructing Algos 3: Quote Stuffing As A Means Of Restoring Arbitrageable Latency; Or Is The CQS TRYING To Crash The Market?
Submitted by The World Complex Deconstructing Algos 3: Quote Stuffing As A Means ... ComplexDeconstructing Algos 3: Quote Stuffing As A Means Of Restoring Arbitrageable LatencyIn a recent article Nanex has ... at least 33% too low. 3. An algo is testing how much more quote noise it needs to generate to cause ...
[ ] Story - Tyler Durden - 07/08/2011 - 22:08 - 63 comments - 0 attachments
Guest Post: Deconstructing Algos, Part 1
Submitted by The World Complex Deconstructing algos, part 1 The third part ... Natural Gas Submitted by The World ComplexDeconstructing algos, part 1 The third part of the series ... are critical to the decision-making module of the algo. The reconstructed phase space The difficulties ...
[ ] Story - Tyler Durden - 06/24/2011 - 21:16 - 82 comments - 0 attachments
Gold Tumbles More Than $100 As $1700 Stops Triggered
to algo driven liquidations following the earlier described shift in sentiment, or has some assistance ... whispers? Felt Any MFG style whispers? Felt like a bit more than algos. More like a company iquidation ...
( ) Application: possible training course for supervisors and regulators around the world
I shall be adding to this list of references from time to time and reorganising its entirety when appropriate:
( ) IOSCO'S Recommendation for Standard Regulation on HFTs
Regulatory Issues Raised by the Impact of Technological Changes on Market Integrity and Efficiency - Consultative Report
OISU - ISOCO (July 2011)
http://www.iosco.org/library/pubdocs/pdf/IOSCOPD354.pdf
( ) SEC Report on May 6, 2010 Flash Crash (100930)
http://www.sec.gov/news/studies/2010/marketevents-report.pdf
( ) Zerohedge (100623): http://www.zerohedge.com/article/how-hft-quote-stuffing-caused-market-crash-may-6-and-threatens-destroy-entire-market-any-mom
( ) Nanex Analysis of the Flash Crash (100618): http://www.nanex.net/20100506/FlashCrashAnalysis_CompleteText.html
[ ] pay particular attention to "quote stuffing" which Nanex says should be banned: http://www.nanex.net/20100506/FlashCrashAnalysis_Part4-1.html
( ) Nanex Analysis of the SEC's Flash Crash (May 6, 2010) Report of Sept 30, 2010 (120412):
( ) Email exchange on the definition of LIQUIDITY: http://www.nanex.net/aqck/2977.html
( ) Nanex updated analysis on April 11, 2011--check out the 2nd chart especially when Wadell and Clarke whom the SEC has blamed for the Flash Crash and the W&C has accepted such blame, could NOT PHYSICALLY be the one who was involved in the perpetration of the flash crash! http://www.nanex.net/FlashCrashFinal/FlashCrashAnalysis_WR_Update.html
Background Readings:
[ ] http://www.zerohedge.com/article/guest-post-deconstructing-algos-part-1
[ ] http://www.zerohedge.com/article/guest-post-deconstructing-algos-part-2-leveraging-chaos-high-frequency-arbitrage-opportuniti
[ ] http://www.zerohedge.com/article/guest-post-deconstructing-algos-3-quote-stuffing-means-restoring-arbitrageable-latency-or-cq
[ ] http://www.zerohedge.com/news/guest-post-deconstructing-algos-part-4-phase-space-reconstructions-cnty-busted-trades-suggests-
HFT REVIEW White papers, academic and industry reports
ACADEMIC ARTICLES ON POINT
http://www.hftreview.com/pg/main/academic-studies/
INVESTIGATIONS
[ ] SEC Probes Ties to High Speed Traders
http://online.wsj.com/article/SB10001424052702303816504577321864050711038.html
NY TIMES ARTICLES
135 articles on high frequency trading as of April 4, 2012
http://topics.nytimes.com/topics/reference/timestopics/subjects/h/high_frequency_algorithmic_trading/index.html
EUROPEAN REGULATIONS
[ ] MiFID 2 Barnier
http://hft.thomsonreuters.com/2010/09/23/eus-barnier-throws-spotlight-on-dark-pool-trades/
REUTERS THOMSON HFT NEWS
http://hft.thomsonreuters.com/
WHARTON article
http://knowledge.wharton.upenn.edu/article.cfm?articleid=2345
INSTITUTIONAL INVESTOR
10 articles
http://www.iijournals.com/page/HighFrequencyTrading
ACADEMIC PAPERS
[ ] Conflicting Codes and Codings
How Algorithmic Trading Is Reshaping Financial Regulation
Marc Lenglet
Abstract
Contemporary financial markets have recently witnessed a sea change with the ‘algorithmic revolution’, as trading automats are used to ease the execution sequences and reduce market impact. Being constantly monitored, they take an active part in the shaping of markets, and sometimes generate crises when ‘they mess up’ or when they entail situations where traders cannot go backwards. Algorithms are software codes coding practices in an IT significant ‘textual’ device, designed to replicate trading patterns. To be accepted, however, they need to comply with regulatory texts, which are nothing else but codes of conduct coding accepted practices in the markets. In this article, I draw on ethnographic fieldwork in order to open these black boxes, while trying to describe their existence as devices encapsulating several points of views. I address the question of a possible misalignment between those visions, and more specifically try to draw the consequences raised by such discrepancies as regards the future of financial regulation.
algorithmic trading codes of conduct codings financial markets practices regulation
Articles citing this article
Codes and Codings in Crisis: Signification, Performativity and Excess
Theory, Culture & Society November 1, 2011 28: 3-23
AbstractFull Text (PDF)
[ ] Investigating Financial Fraud in High Frequency Trading
Afroditi Katika
University of Manchester
Babis Theodoulidis
University of Manchester - Manchester Business School
David Diaz
University of Manchester - Manchester Business School; Universidad de Chile - Escuela de Economia y Negocios
December 20, 2011
Abstract:
Market monitoring is a very important process to the stock market. It is necessary in order to verify that all trades comply with the existing rules, as well as to detect any act of manipulation. Recently, a new kind of trading has emerged, High Frequency Trading, which allows traders to place and execute orders within milliseconds via a program running in a computer. It is doubtful whether existent market systems are capable of detecting inconsistencies in trades at this speed. This project has attempted to propose a design of a detection engine that could be incorporated to a monitoring framework so as to accommodate High Frequency trades. Understanding the field of stock markets and High Frequency Trading was a crucial part of this project. Since it is such a recent phenomenon with no confirmed cases (to the best of our knowledge) of market manipulation, we attempted to answer whether there are certain conditions that could benefit market manipulators. We used business intelligence techniques to analyse historical data and discover what sort of indications our detection engine should look for. Our results show that there have been violations of regulations that were not blocked in real-time which proves the inefficiency of current market monitoring systems. We also prove that an extreme number of orders within seconds can delay an exchange’s processes and systems. In the end we propose a design that takes those results into consideration.
Keywords: high frequency trading, flash crash, quote stuffing, financial markets, market manipulation, fraud detection, market monitoring, market surveillance
Working Paper Series
Date posted: December 20, 2011
Suggested Citation
Katika, Afroditi, Theodoulidis, Babis and Diaz, David, Investigating Financial Fraud in High Frequency Trading (December 20, 2011). Available at SSRN: http://ssrn.com/abstract=1974911
[ ] On the Dark Side of the Market: Identifying and Analyzing Hidden Order Placements
Nikolaus Hautsch
Humboldt-Universität zu Berlin; CASE - Center for Applied Statistics and Economics; CFS
Ruihong Huang
Humboldt University of Berlin
February 8, 2012
Abstract:
Trading under limited pre-trade transparency becomes increasingly popular on financial markets. We provide first evidence on traders' use of (completely) hidden orders which might be placed even inside of the (displayed) bid-ask spread. Employing TotalView-ITCH data on order messages at NASDAQ, we propose a simple method to conduct statistical inference on the location of hidden depth and to test economic hypotheses. Analyzing a wide cross-section of stocks, we show that market conditions reflected by the (visible) bid-ask spread, (visible) depth, recent price movements and trading signals significantly affect the aggressiveness of 'dark' liquidity supply and thus the 'hidden spread'. Our evidence suggests that traders balance hidden order placements to (i) compete for the provision of (hidden) liquidity and (ii) protect themselves against adverse selection, front-running as well as 'hidden order detection strategies' used by high-frequency traders. Accordingly, our results show that hidden liquidity locations are predictable given the observable state of the market.
Number of Pages in PDF File: 43
Keywords: limit order market, hidden liquidity, high-frequency trading, non-display order, iceberg orders
JEL Classifications: G14, C24, C25, G17
Working Paper Series
Date posted: February 13, 2012
Suggested Citation
Hautsch, Nikolaus and Huang, Ruihong, On the Dark Side of the Market: Identifying and Analyzing Hidden Order Placements (February 8, 2012). Available at SSRN: http://ssrn.com/abstract=2004231 or http://dx.doi.org/10.2139/ssrn.2004231
CASE STUDIES
[ ] BATS Take-down
http://www.zerohedge.com/news/skynet-wars-how-nasdaq-algo-destroyed-bats
[ ] http://www.zerohedge.com/news/presenting-todays-21-least-mini-flash-crashes
[ ] http://www.zerohedge.com/article/fractal-limit-order-buster-latest-market-manipulation-algo-gimmick
[ ] Man Vs Machine: How Each Sees The Stock Market
Submitted by Tyler Durden on 04/03/2012
available at: http://www.zerohedge.com/news/man-vs-machine-how-each-sees-stock-market
[ ] http://www.zerohedge.com/news/fractal-algo-strikes-again-time-impacts-popular-bond-bear-etf-tbt
[ ] http://www.zerohedge.com/news/stop-loss-terminator-algo-reemerges-picks-national-bank-greece-todays-victim
[ ] http://www.zerohedge.com/news/dear-hft-please-explain
[ ] http://www.zerohedge.com/news/step-right-its-hft-whack-mole-time
[ ] http://www.zerohedge.com/news/whack-mole-algo-back
[ ] http://www.zerohedge.com/article/are-hft-algos-taking-aim-dominating-and-manipulating-wonderful-world-etfs-next
[ ] http://www.zerohedge.com/article/visualizing-market-topology-video-real-time-exchange-routing
[ ] http://www.zerohedge.com/news/does-high-frequency-trading-adds-market-liquidity-vote-here
[ ] http://www.zerohedge.com/article/hft-now-business-frontrunning-each-others-regulatory-capture
[ ] http://www.zerohedge.com/article/caught-act-hft-option-algos-observed-frontrunning-todays-pmi-release
[ ] http://www.zerohedge.com/article/some-observations-spy-vwap-and-block-manipulation-fsa-launches-probe-front-running-block-tra
[ ] http://www.zerohedge.com/article/no-its-not-nat-gas-fractal-algo-nanex-discloses-very-ominous-implications-todays-berserk-cru
[ ] http://www.zerohedge.com/article/another-algo-gone-wild
RANDOM QUOTES:
[ ] Guest Post: Deconstructing Algos, Part 4 -Phase Space Reconstructions Of CNTY Busted Trades Suggests High Speed Gang-Bangs In The Market
Submitted by The World Complex Deconstructing Algos, Part 4: Phase Space ... Volatility Submitted by The World ComplexDeconstructing Algos, Part 4: Phase Space Reconstructions ... the algos picked up by Nanex on June 21, 2011 in CNTY using the data appended here . ...
Story - Tyler Durden - 07/31/2011 - 17:43 - 39 comments - 0 attachments
[ ] Guest Post: Deconstructing Algos, Part 2: Leveraging Chaos Into High-Frequency Arbitrage Opportunities
Submitted by The World Complex Deconstructing Algos, Part 2: Leveraging Chaos Into High-Frequency Arbitrage Opportunities The recent elegant explanation for the activities of the HFT algos ... Natural Gas Submitted by The World ComplexDeconstructing Algos, Part 2: Leveraging Chaos ...
[ ] Story - Tyler Durden - 07/01/2011 - 00:21 - 32 comments - 0 attachments
Guest Post: Deconstructing Algos 3: Quote Stuffing As A Means Of Restoring Arbitrageable Latency; Or Is The CQS TRYING To Crash The Market?
Submitted by The World Complex Deconstructing Algos 3: Quote Stuffing As A Means ... ComplexDeconstructing Algos 3: Quote Stuffing As A Means Of Restoring Arbitrageable LatencyIn a recent article Nanex has ... at least 33% too low. 3. An algo is testing how much more quote noise it needs to generate to cause ...
[ ] Story - Tyler Durden - 07/08/2011 - 22:08 - 63 comments - 0 attachments
Guest Post: Deconstructing Algos, Part 1
Submitted by The World Complex Deconstructing algos, part 1 The third part ... Natural Gas Submitted by The World ComplexDeconstructing algos, part 1 The third part of the series ... are critical to the decision-making module of the algo. The reconstructed phase space The difficulties ...
[ ] Story - Tyler Durden - 06/24/2011 - 21:16 - 82 comments - 0 attachments
Gold Tumbles More Than $100 As $1700 Stops Triggered
to algo driven liquidations following the earlier described shift in sentiment, or has some assistance ... whispers? Felt Any MFG style whispers? Felt like a bit more than algos. More like a company iquidation ...
Thursday 12 April 2012
Default Invariance: Product & Sum Modules - Sans Esquisses
Default Invariance:
Product and Sum Category Theory Models of Financial Contracts
Product Model: Pay or Not-Pay
Sum Model: Financial Legal Remedies
1. Recall the Arrow-Debreu-Sharpe model of t0 to t1 corresponding to the state of initial financial contract in a world of infinite contingent states and the state of pay, respectively.
2. We improved the ADS Model to a Default Invariance Model where the t1 state is now bi-valued to include (a) Pay and (b) Not-Pay, i.e. P and -P.
3. If t1 results in -P then the infinite contingent states continues at t1. This is equivalent (or isomorphic) to the infinite-contingent-states being multiplied by 1.
4. If t1 results in P then the infinite contingent states is annihilated and the certainty of payment makes the financial contract certain and therefore, immediately disengages from the infinitely contingent states of world. This is equivalent (or isomorphic) to the inifinite-contingent-states being multiplied by 0.
5. The 2-state at t1 default invariance model can be further specified in terms of Product and Sum. [This is going to get a bit technical, I warn you.]
Definition of Product
An object P together with a pair of maps P1:P->B1, and P2:P->B2 is called a product of B1 and B2 if for each object X and each pair of maps f1:X->B1, f2:X->B2, there is exactly one map f:X->P for which both f1=P1f and f2=P2f. [See Lawvere & Schanuel, 2009, p. 217.]
[I'll insert a diagram later. Hint: it looks like a chevron with X on the left and an arrow from X to P which is, another arrow from X to B1 labelled f1, an arrow P1 from P to B1, an arrow from X to B2 labelled f2, and an arrow P2 from P to B2.]
6. Given this definition of Product, we can now apply what we stated in an earlier blog that payment of a financial contract makes it certain and therefore, takes it out of the realm of uncertainty and is no longer part of ("resides in") a world of infinite contingent states. Thus, an occurrence of payment is equivalent to the value of 0 in the infinite contingent world. In our Product Diagram B1 = (Infinite-Contigency) x (0). Another way of saying this is B1 = Uncertainty x 0, which means, no more uncertainty. This valuation is not what Sharpe and others had supposed, and had in fact given payment the value of 1, which leads to inconsistent and contradictory results.
7. Also, we can see that non-payment or not-paying at t1 means that the infinite-contingent-states of the world continues at t1. This is equivalent to: (infinite-contingent-states) x (1). So, non-payment is actually an identity morphism. In our Default Invariance Product Diagram, B2 = 1. Strangely, f2 will have to be equivalent to infinite contingency divided by infinite contingency.
8. As a sum, we have the following definition:
A pair j1: B1->S, j2; B2->S, of maps in a category makes S a sum of B1 and B2 if for ach object Y and each pair g1:B1-Y, g2:B2-Y, there is exactly one map g:S->Y for which both g1 = gj1 and g2 = gj2. [See Lawvere & Schanuel (2009) Conceptual Mathematics, p. 222]
It is my contention that a legal remedy to a financial contract has the form of a sum as above, where Y is a legal remedy and B1 and B2 to breach and not-breach situations of the contract. This is of course a first approximation of a legal risk theory.
9. The virtue of a Product and a Sum Model for the fundamental and universal unit of law and finance is that by putting them together THROUGH TIME (that is, from t0, t1, t2,...tn) we begin to have a view of how law and finance may be seen under one perspective that allows for both (1) simplification and anticipation of direct results -- i.e., "rough and ready" calculations that border on immediate insight through very complex legal and financial phenomena; and (2) a very detailed and rigorous, bookkeeping or tracking methodology to ensure that our predictions make sense and are grounded on facts.
Product and Sum Category Theory Models of Financial Contracts
Product Model: Pay or Not-Pay
Sum Model: Financial Legal Remedies
1. Recall the Arrow-Debreu-Sharpe model of t0 to t1 corresponding to the state of initial financial contract in a world of infinite contingent states and the state of pay, respectively.
2. We improved the ADS Model to a Default Invariance Model where the t1 state is now bi-valued to include (a) Pay and (b) Not-Pay, i.e. P and -P.
3. If t1 results in -P then the infinite contingent states continues at t1. This is equivalent (or isomorphic) to the infinite-contingent-states being multiplied by 1.
4. If t1 results in P then the infinite contingent states is annihilated and the certainty of payment makes the financial contract certain and therefore, immediately disengages from the infinitely contingent states of world. This is equivalent (or isomorphic) to the inifinite-contingent-states being multiplied by 0.
5. The 2-state at t1 default invariance model can be further specified in terms of Product and Sum. [This is going to get a bit technical, I warn you.]
Definition of Product
An object P together with a pair of maps P1:P->B1, and P2:P->B2 is called a product of B1 and B2 if for each object X and each pair of maps f1:X->B1, f2:X->B2, there is exactly one map f:X->P for which both f1=P1f and f2=P2f. [See Lawvere & Schanuel, 2009, p. 217.]
[I'll insert a diagram later. Hint: it looks like a chevron with X on the left and an arrow from X to P which is
6. Given this definition of Product, we can now apply what we stated in an earlier blog that payment of a financial contract makes it certain and therefore, takes it out of the realm of uncertainty and is no longer part of ("resides in") a world of infinite contingent states. Thus, an occurrence of payment is equivalent to the value of 0 in the infinite contingent world. In our Product Diagram B1 = (Infinite-Contigency) x (0). Another way of saying this is B1 = Uncertainty x 0, which means, no more uncertainty. This valuation is not what Sharpe and others had supposed, and had in fact given payment the value of 1, which leads to inconsistent and contradictory results.
7. Also, we can see that non-payment or not-paying at t1 means that the infinite-contingent-states of the world continues at t1. This is equivalent to: (infinite-contingent-states) x (1). So, non-payment is actually an identity morphism. In our Default Invariance Product Diagram, B2 = 1. Strangely, f2 will have to be equivalent to infinite contingency divided by infinite contingency.
8. As a sum, we have the following definition:
A pair j1: B1->S, j2; B2->S, of maps in a category makes S a sum of B1 and B2 if for ach object Y and each pair g1:B1-Y, g2:B2-Y, there is exactly one map g:S->Y for which both g1 = gj1 and g2 = gj2. [See Lawvere & Schanuel (2009) Conceptual Mathematics, p. 222]
It is my contention that a legal remedy to a financial contract has the form of a sum as above, where Y is a legal remedy and B1 and B2 to breach and not-breach situations of the contract. This is of course a first approximation of a legal risk theory.
9. The virtue of a Product and a Sum Model for the fundamental and universal unit of law and finance is that by putting them together THROUGH TIME (that is, from t0, t1, t2,...tn) we begin to have a view of how law and finance may be seen under one perspective that allows for both (1) simplification and anticipation of direct results -- i.e., "rough and ready" calculations that border on immediate insight through very complex legal and financial phenomena; and (2) a very detailed and rigorous, bookkeeping or tracking methodology to ensure that our predictions make sense and are grounded on facts.
Tuesday 3 April 2012
Platonic Signage: From Discrete Algebraic Individual Complaints to Continuous Geometric Social Solutions
Or, Infinite Smoothness: From The Discrete Complaints of Individuality to The Ironic Continuum of Small Rules
1. I think it's in book 2 or 3 of The Republic that Plato makes a rhetorical analogy that is engrained in the way we argue and complain about ourselves and our relations to society. He asks to transfer the argument about whether a person's happiness depends on power and money rather than virtue (that is, knowledge of the good) to a much larger body that can be dissected objectively, namely, the body of society. The move from examining the personal body and its object of happiness (what we might now call psychology) to the social body and its aim of good government, may seem quite weak, for how can we trust in an answer to a problem which is at a level different from the problem itself. The problem is more particular and local than the solution which is general and indeed, allegedly universal.
2. This move has bothered me for 42 years. Now, I think I have an answer to the quandary both at the substantive and procedural levels. And both technically can be viewed from what we call a category theory. We can also immediately understand Plato's overall strategy as a movement from a local composition in algebra to a general conception of geometry. (There is an apocryphal saying that the signage above Plato's Academy said something to the effect, "Let no one without Geometry enter [this space]."
3. I would also temper this interpretation with a couple caveats. First, Plato though genius of the first degree did not have the devices necessary to found category theory. Second, when I call out the term of art, category theory, I mean in the first and foremost instance, the conceptualisation of certain data about objects, arrows (morphisms), the associativity axiom [(a*b)*c = a*(b*c)], and the identity axiom [a*I = a = 1*a]. In its most austere form and substance, namely, in diagrams or sketches ("esquisses") very very complex structures that would not be very comprehensible in a grammatical English are very evidently laid out like Dr. Seuss drawings. One can for example re-wire quantum mechanical expressions rather naturally in category theory and understand how so-complex financial contracts work in an infinitely contingent world.
4. Coming back to the Platonic move from small (individual) to big (society), we recall Socrates' reason for this move was because he was trapped. The two nephews of Plato, x and y, [i can't remember their names but will look them up later--maybe Glaucon and Adimentaus?] had argued so eloquently and convincingly that at the PERSONAL level only power and money counted for anything in a real person's real happiness. This was an argument based on personal observation ("what is evidently and evidentially true"). So, Platonic philosophy based whole heartedly on one's personal knowledge and education could hardly win against someone whose argument was based on personally observed facts.
5. Socrates had to go a level up. Plato through Socrates was making an argument about the SPACE around the individual, the interconnections, the networks, the various specialised objects ("specialists are better for the good of the whole society than the inefficient workings of generalists"), and how ultimately, this led to an analysis of governance, from benevolent dictator to timocracy, oligarchy, democracy and tyrant. All of this was rounded by the question asked of Socrates, "And what if none of what you have imagined comes about?" Socrates' answer again is of a SPACE, "Well then, we have not wasted time, because forever and a day, people will now know where they should be heading." In other words, Socrates had literally given future generations a map to travel, with signposts and monuments. Now, just as no one on the tube in London can say that the tube maps are what the tubes and tube lines are, we can't say that Plato's Republic describes exactly what is front of us. Much depends on our understanding of how to make the correspondences between the map and our own presence or location. We use the map as a guide to help make sure we steer ourselves to a particular destination.
6. The more general meaning and thus, philosophical import of the move from individual psyche to the social space is in the form of generalisation. Note that the rules defining the linkages in the local space, i.e., the relations between individuals, which in a strict sense might be defined as "rules" establish a structure which is the definition of the entire space in which any and all individuals exist. This movement from particular individual mind to the structures which link us together may appear to be a type of algebraic expression of composition, that is, combinations of bilateral transactions. But the point is that these groups defined by rules when applied generally literally create a geometry of social space. It is a space that is topologically continuous.
7. As we say in the old lingo, "from the many to the one." We can now understand this as a movement from the particular algebraic rules that appear discrete in form but are actually, when taken together, define the infinite smoothness of the skin of reality. The slogan here is, "small rules define big space."
8. As a meditation one might take the slogan to its limit in breath, balance and humour.
1. I think it's in book 2 or 3 of The Republic that Plato makes a rhetorical analogy that is engrained in the way we argue and complain about ourselves and our relations to society. He asks to transfer the argument about whether a person's happiness depends on power and money rather than virtue (that is, knowledge of the good) to a much larger body that can be dissected objectively, namely, the body of society. The move from examining the personal body and its object of happiness (what we might now call psychology) to the social body and its aim of good government, may seem quite weak, for how can we trust in an answer to a problem which is at a level different from the problem itself. The problem is more particular and local than the solution which is general and indeed, allegedly universal.
2. This move has bothered me for 42 years. Now, I think I have an answer to the quandary both at the substantive and procedural levels. And both technically can be viewed from what we call a category theory. We can also immediately understand Plato's overall strategy as a movement from a local composition in algebra to a general conception of geometry. (There is an apocryphal saying that the signage above Plato's Academy said something to the effect, "Let no one without Geometry enter [this space]."
3. I would also temper this interpretation with a couple caveats. First, Plato though genius of the first degree did not have the devices necessary to found category theory. Second, when I call out the term of art, category theory, I mean in the first and foremost instance, the conceptualisation of certain data about objects, arrows (morphisms), the associativity axiom [(a*b)*c = a*(b*c)], and the identity axiom [a*I = a = 1*a]. In its most austere form and substance, namely, in diagrams or sketches ("esquisses") very very complex structures that would not be very comprehensible in a grammatical English are very evidently laid out like Dr. Seuss drawings. One can for example re-wire quantum mechanical expressions rather naturally in category theory and understand how so-complex financial contracts work in an infinitely contingent world.
4. Coming back to the Platonic move from small (individual) to big (society), we recall Socrates' reason for this move was because he was trapped. The two nephews of Plato, x and y, [i can't remember their names but will look them up later--maybe Glaucon and Adimentaus?] had argued so eloquently and convincingly that at the PERSONAL level only power and money counted for anything in a real person's real happiness. This was an argument based on personal observation ("what is evidently and evidentially true"). So, Platonic philosophy based whole heartedly on one's personal knowledge and education could hardly win against someone whose argument was based on personally observed facts.
5. Socrates had to go a level up. Plato through Socrates was making an argument about the SPACE around the individual, the interconnections, the networks, the various specialised objects ("specialists are better for the good of the whole society than the inefficient workings of generalists"), and how ultimately, this led to an analysis of governance, from benevolent dictator to timocracy, oligarchy, democracy and tyrant. All of this was rounded by the question asked of Socrates, "And what if none of what you have imagined comes about?" Socrates' answer again is of a SPACE, "Well then, we have not wasted time, because forever and a day, people will now know where they should be heading." In other words, Socrates had literally given future generations a map to travel, with signposts and monuments. Now, just as no one on the tube in London can say that the tube maps are what the tubes and tube lines are, we can't say that Plato's Republic describes exactly what is front of us. Much depends on our understanding of how to make the correspondences between the map and our own presence or location. We use the map as a guide to help make sure we steer ourselves to a particular destination.
6. The more general meaning and thus, philosophical import of the move from individual psyche to the social space is in the form of generalisation. Note that the rules defining the linkages in the local space, i.e., the relations between individuals, which in a strict sense might be defined as "rules" establish a structure which is the definition of the entire space in which any and all individuals exist. This movement from particular individual mind to the structures which link us together may appear to be a type of algebraic expression of composition, that is, combinations of bilateral transactions. But the point is that these groups defined by rules when applied generally literally create a geometry of social space. It is a space that is topologically continuous.
7. As we say in the old lingo, "from the many to the one." We can now understand this as a movement from the particular algebraic rules that appear discrete in form but are actually, when taken together, define the infinite smoothness of the skin of reality. The slogan here is, "small rules define big space."
8. As a meditation one might take the slogan to its limit in breath, balance and humour.
Sunday 1 April 2012
The Baby Blue Eyes of the Universe: Philosophical Calculations of Governance and Infinity
Philosophical Calculations
1. The great Greek philosophers Plato and Aristotle identified the problem of (1) how to distinguish between a benevolent dictator and a tyrant, and (2) how to determine the continuous from the discrete, respectively. Plato's insight into the problem of governance comes in books VIII to IX of the Republic, and Aristotle's conundrums of the infinity of points in space and time come from his recollection of the paradoxes of Zeno of Elea in the first books of the Metaphysics.
2. Both problems cut through what might be called epistemology, or the limits of our knowledge. For example, how can we possibly distinguish between two persons who say, "believe me for I know the good." Answer: we can't unless we ourselves (read here, each and every one of us) have educated ourselves enough to make this discrimination. No one can give us this knowledge. We have to come upon it ourselves. We have to be ruthlessly Descartian. In terms of the pure metaphysical problem of infinity of points, this becomes a matter of discriminating between the continuous and the discrete, between the one and the many. Modernly, we can resolve this tension to an awfully abstract sense of proportions if we move diligently from nominal, interval, ordinal and rational scales, and have some notation to help us with the precise bookkeeping (a type of Thesesusian string in the minotaur's cave) so we can accurately account for how apparently different forms are essentially together in a weakened form of equivalence. A few algebraic expressions define the local key to the global code of a geometry, and the geometry gives us an insight to the totality of global meanings of finite algebraic expressions. The Buddha says this by carrying a flower, the mathematicus writes a few squiggles, a few angels sing, and the infant's eyes reflect the absolute depth of the pure blue sky.
3. Belief in a stranger tells us something about us. We can never know the other except through abstractions. But these abstractions are obviously not the other. Don't be greedy. Let the composition come. What comes naturally is already embedded and as some say, the one. To wait for the one is to let the universe do the calculation. To ride the winds, to move in every direction, is the way nature calculates answers directly through us.
1. The great Greek philosophers Plato and Aristotle identified the problem of (1) how to distinguish between a benevolent dictator and a tyrant, and (2) how to determine the continuous from the discrete, respectively. Plato's insight into the problem of governance comes in books VIII to IX of the Republic, and Aristotle's conundrums of the infinity of points in space and time come from his recollection of the paradoxes of Zeno of Elea in the first books of the Metaphysics.
2. Both problems cut through what might be called epistemology, or the limits of our knowledge. For example, how can we possibly distinguish between two persons who say, "believe me for I know the good." Answer: we can't unless we ourselves (read here, each and every one of us) have educated ourselves enough to make this discrimination. No one can give us this knowledge. We have to come upon it ourselves. We have to be ruthlessly Descartian. In terms of the pure metaphysical problem of infinity of points, this becomes a matter of discriminating between the continuous and the discrete, between the one and the many. Modernly, we can resolve this tension to an awfully abstract sense of proportions if we move diligently from nominal, interval, ordinal and rational scales, and have some notation to help us with the precise bookkeeping (a type of Thesesusian string in the minotaur's cave) so we can accurately account for how apparently different forms are essentially together in a weakened form of equivalence. A few algebraic expressions define the local key to the global code of a geometry, and the geometry gives us an insight to the totality of global meanings of finite algebraic expressions. The Buddha says this by carrying a flower, the mathematicus writes a few squiggles, a few angels sing, and the infant's eyes reflect the absolute depth of the pure blue sky.
3. Belief in a stranger tells us something about us. We can never know the other except through abstractions. But these abstractions are obviously not the other. Don't be greedy. Let the composition come. What comes naturally is already embedded and as some say, the one. To wait for the one is to let the universe do the calculation. To ride the winds, to move in every direction, is the way nature calculates answers directly through us.
Friday 30 March 2012
The Eternal Spring
For the 102nd session of the Philosophical Foundations of Law and Finance, to be held from 6 to 8pm tonight, Friday March 30th 2012, in room 501, University of Westminster campus, we will: (1) collect the LLM dissertation titles from students and (2) examine the causes of the perrenial Great War (making peace between our genetics and our genuine spiritual being) and the ongoing Great Depression (making war between superficial consumerism and our lives).
As a philosophy student studying Plato and Aristotle in Princeton during the Vietnam War, it became obvious to me that a lot of my very brilliant colleagues who'd received princely educations believing that they would become very rich (millionaire-billionaires adjusting for inflation), movie stars, rock stars and presidents, would become relatively average and sedate, if not sedated, and those who did not fall under medication, would become very pissed off, having squandered their God-given talents chasing the meaninglessness of empty suits.
Today, the Arab spring is just one of the global blooms of corrupt political-economic systems where holier than thou public servants have hundreds of billions of dollars of personal wealth while their poor citizen have not even one ounce of zakat, and as the political elite have continuously "bailed out" the bankers in the US and Europe, we have immense bubbles that can be resolved only in terms of debt forgiveness (where bankers take the hit) or more fascistic totalitarianism (where the good taxpaying citizens are debt enslaved). To clarify these choices, we have some beautifully illustrated lectures by David McWilliams of Punk Economics via Zerohedge:
http://www.zerohedge.com/news/how-europe-has-evolved-democracy-bankocracy-and-why-austerity-will-lead-chaos
http://www.zerohedge.com/news/europes-cash-trash-ltro-scam-and-indentured-servitude-citizenry
http://www.zerohedge.com/news/liquidity-and-false-recovery
Enjoy your spring wherever you are and be prepared for another kind of spring coming soon to your door.
Ciao
Joe
As a philosophy student studying Plato and Aristotle in Princeton during the Vietnam War, it became obvious to me that a lot of my very brilliant colleagues who'd received princely educations believing that they would become very rich (millionaire-billionaires adjusting for inflation), movie stars, rock stars and presidents, would become relatively average and sedate, if not sedated, and those who did not fall under medication, would become very pissed off, having squandered their God-given talents chasing the meaninglessness of empty suits.
Today, the Arab spring is just one of the global blooms of corrupt political-economic systems where holier than thou public servants have hundreds of billions of dollars of personal wealth while their poor citizen have not even one ounce of zakat, and as the political elite have continuously "bailed out" the bankers in the US and Europe, we have immense bubbles that can be resolved only in terms of debt forgiveness (where bankers take the hit) or more fascistic totalitarianism (where the good taxpaying citizens are debt enslaved). To clarify these choices, we have some beautifully illustrated lectures by David McWilliams of Punk Economics via Zerohedge:
http://www.zerohedge.com/news/how-europe-has-evolved-democracy-bankocracy-and-why-austerity-will-lead-chaos
http://www.zerohedge.com/news/europes-cash-trash-ltro-scam-and-indentured-servitude-citizenry
http://www.zerohedge.com/news/liquidity-and-false-recovery
Enjoy your spring wherever you are and be prepared for another kind of spring coming soon to your door.
Ciao
Joe
Monday 26 March 2012
The Consilience of Financial-Economics: Happiness
Title: The Consilience of Financial-Economic: Happiness
In a very brief article by David Sloan Wilson entitled, "A Tale of Two Classics," [New Scientist, 24 March 2012, 30-31], he reviews two influential academic articles:
[ ] Milton Friedman's essay, "The Methodology of Positive Economics," (1953); and
[ ] Stephen Jay Gould and Richard Lewontin's article, "The Spandrels of San Marcos and The Panglossian Paradigm."
The former sets out the classic statement on homo oeconomicus as a species that acts as if the assumptions of orthodox economic theory were true when in the individual cases it is manifestly untrue. This distinction in size is very important and may help explain the differences in the opinion of classical versus behavioural theorists.
The latter is a critique of the use of the argument of adaptation, where theorists fail to distinguish again between different levels of phenomena. Thus, the general adaptive rule that desert animals are all likely to have similar hues for camouflage does not mean that all desert animals are necessarily genetically related. The distinction au fond here is between long-term and proximate cause.
Both papers and D.S. Wilson's own comments warn about what Aristotle first called "metaphysics." Indeed, the concept of cause and its four variations (formal, essential-substantive, efficient and teleological) were practically invented by Aristotle. But the one big point Wilson makes is the need for CONSILIENCE (I believe this term was first coined and made popular by Edward O. Wilson, the great ant-scientist at Harvard). Consilience is the test of an idea in light of its unity with the other sciences.
I find consilience completely absent in business schools and relegated to the fringe in US and UK law schools. This is the main reason why business school and law school curricula appear superficial and are probably marked for obsolescence in the next decade or two. Given what D.S. Wilson says above, it is not difficult to see how the technical financial theology taught in US and European business schools could easily lead to numerous frauds and deceits in the financial industry. The desert is general financial-economic theory and its camouflaged animals are the bad human animals. For example, technical financial textbooks trot out the ideas that "arbitrage" and "net present value" are themselves self-justifying aims within financial theory. These little but significant facts tell us that consilience is utterly lacking in financial theory.
The adjustments required for the benefit of the rest of society should be in the form of regulation, but here, if the game keepers turn a blind eye, the outcome at best will be small pockets of stability for the very rich in a sea of instantaneous instabilities for the rest and mostly poor.
The long-term solution aims at consilience, but without the ancient Platonic ideals of social comity or the modern Bhutanese concept of 'happy economy', we have only ourselves to blame for failing to distinguish proximate from long term causes of misery and happiness.
In a very brief article by David Sloan Wilson entitled, "A Tale of Two Classics," [New Scientist, 24 March 2012, 30-31], he reviews two influential academic articles:
[ ] Milton Friedman's essay, "The Methodology of Positive Economics," (1953); and
[ ] Stephen Jay Gould and Richard Lewontin's article, "The Spandrels of San Marcos and The Panglossian Paradigm."
The former sets out the classic statement on homo oeconomicus as a species that acts as if the assumptions of orthodox economic theory were true when in the individual cases it is manifestly untrue. This distinction in size is very important and may help explain the differences in the opinion of classical versus behavioural theorists.
The latter is a critique of the use of the argument of adaptation, where theorists fail to distinguish again between different levels of phenomena. Thus, the general adaptive rule that desert animals are all likely to have similar hues for camouflage does not mean that all desert animals are necessarily genetically related. The distinction au fond here is between long-term and proximate cause.
Both papers and D.S. Wilson's own comments warn about what Aristotle first called "metaphysics." Indeed, the concept of cause and its four variations (formal, essential-substantive, efficient and teleological) were practically invented by Aristotle. But the one big point Wilson makes is the need for CONSILIENCE (I believe this term was first coined and made popular by Edward O. Wilson, the great ant-scientist at Harvard). Consilience is the test of an idea in light of its unity with the other sciences.
I find consilience completely absent in business schools and relegated to the fringe in US and UK law schools. This is the main reason why business school and law school curricula appear superficial and are probably marked for obsolescence in the next decade or two. Given what D.S. Wilson says above, it is not difficult to see how the technical financial theology taught in US and European business schools could easily lead to numerous frauds and deceits in the financial industry. The desert is general financial-economic theory and its camouflaged animals are the bad human animals. For example, technical financial textbooks trot out the ideas that "arbitrage" and "net present value" are themselves self-justifying aims within financial theory. These little but significant facts tell us that consilience is utterly lacking in financial theory.
The adjustments required for the benefit of the rest of society should be in the form of regulation, but here, if the game keepers turn a blind eye, the outcome at best will be small pockets of stability for the very rich in a sea of instantaneous instabilities for the rest and mostly poor.
The long-term solution aims at consilience, but without the ancient Platonic ideals of social comity or the modern Bhutanese concept of 'happy economy', we have only ourselves to blame for failing to distinguish proximate from long term causes of misery and happiness.
Friday 23 March 2012
Instantaneous Symmetric Risk <=> Dodd Frank Avoidance Scheme
I guess you could make a lot of money helping non-US banks avoid Dodd-Frank Act requirements. See: http://online.wsj.com/article/SB10001424052702303812904577295614224666918.html
Deutsche Bank has always been rather "leveraged" and some estimates say it would have had to come up with between $20 to $40 billion in capital. Instead it gave up its bank holding status so it won't have any FDIC protection. But Title II Orderly Liquidation Authority will be used to liquidate any bank or non-bank posing a systemic risk to the US economy. So the interesting irony here is that by dropping its BHC status and thus lacking federal insurance, hasn't it become instantaneously a danger to the US economy and thus, a target for liquidation? Actually, if I were a benevolent dictator, I'd extract a bit more "taxable value" from Deutsche Bank for making such an obvious avoidance scheme and hold the threat of Title II over its head. Hmm. I doubt severely that the US Fed or the Treasury will consider this argument, but given the powers entrusted them under Title II of the Dodd-Frank Act, they should.
Deutsche Bank has always been rather "leveraged" and some estimates say it would have had to come up with between $20 to $40 billion in capital. Instead it gave up its bank holding status so it won't have any FDIC protection. But Title II Orderly Liquidation Authority will be used to liquidate any bank or non-bank posing a systemic risk to the US economy. So the interesting irony here is that by dropping its BHC status and thus lacking federal insurance, hasn't it become instantaneously a danger to the US economy and thus, a target for liquidation? Actually, if I were a benevolent dictator, I'd extract a bit more "taxable value" from Deutsche Bank for making such an obvious avoidance scheme and hold the threat of Title II over its head. Hmm. I doubt severely that the US Fed or the Treasury will consider this argument, but given the powers entrusted them under Title II of the Dodd-Frank Act, they should.
Wednesday 7 March 2012
From War to Peace and Love Through the Morphism of a Good Massage
The Morphism of Peace and Love => A Good Massage
Alexander, Machiavelli, Sun Tzu, Ghenghis Khan, Tsunetomo and lots of other male dominators from oh so many cultures and periods of history are scary because they USED other human beings as tools for their own ends and because they simply assumed War was inevitable, so they "reasoned," why not just win at whatever the cost which usually meant PRE-EMPTIVE strike. Whatever little bit of DNA-code that "naturally" allows or forces the human species to undertake vast wars against ITSELF should in my opinion be snipped, modified and reconstructed towards that other type of gene which seems to underlie the social-sexual behaviours of Bonobo's. Of course, those religions that support in-group versus out-group mentality through separatist rituals and mystical justification of repression, and thus, are MERELY another manifestation of the SPECIES-KILLER gene, would object violently to this proposal because it would be against their religion. Some enlightened masters figured this "they versus us" mentality is the source of all evil and tried with whatever they had to show others that peace is possible. But this attitude is extremely rare. For example, the founder of Aikido was a master of three martial arts and I studied this art for about 7 years in Honolulu with Yoshioka Sensei. In Aikido, the ethical ideal of no harm to others and yourself is embedded throughout the practice. So, I asked Sensei, "Sensei, you preach 'peace, peace, and love, love' but all we learn in our techniques is only how to kill the other. How can we achieve peace and love when this is all we learn?" His answer is remarkable, "You must learn to stop thinking 'kill, kill' and give your partner a good massage."
Alexander, Machiavelli, Sun Tzu, Ghenghis Khan, Tsunetomo and lots of other male dominators from oh so many cultures and periods of history are scary because they USED other human beings as tools for their own ends and because they simply assumed War was inevitable, so they "reasoned," why not just win at whatever the cost which usually meant PRE-EMPTIVE strike. Whatever little bit of DNA-code that "naturally" allows or forces the human species to undertake vast wars against ITSELF should in my opinion be snipped, modified and reconstructed towards that other type of gene which seems to underlie the social-sexual behaviours of Bonobo's. Of course, those religions that support in-group versus out-group mentality through separatist rituals and mystical justification of repression, and thus, are MERELY another manifestation of the SPECIES-KILLER gene, would object violently to this proposal because it would be against their religion. Some enlightened masters figured this "they versus us" mentality is the source of all evil and tried with whatever they had to show others that peace is possible. But this attitude is extremely rare. For example, the founder of Aikido was a master of three martial arts and I studied this art for about 7 years in Honolulu with Yoshioka Sensei. In Aikido, the ethical ideal of no harm to others and yourself is embedded throughout the practice. So, I asked Sensei, "Sensei, you preach 'peace, peace, and love, love' but all we learn in our techniques is only how to kill the other. How can we achieve peace and love when this is all we learn?" His answer is remarkable, "You must learn to stop thinking 'kill, kill' and give your partner a good massage."
Remember the Parasite: Presentation-Invariance and Degrees of Weakened Equivalence
March 7, 2012
Parasites: Presentation-Invariance and Degrees of Weakened Equivalence
Last night in the seminar on Legal Aspects of International Finance, we had each student read their draft assignments on various aspects of international financial regulations, e.g., the Orderly Liquidation Authority, Whistleblower Incentives and Protection, OTC derivatives under the Dodd -Frank Act, the EC proposal to regulate the OTC derivatives markets, the Volker Rule under Dodd-Frank and the Vickers Report in the UK.
I said to this small but very able group, "I'll be lecturing on Category Theory for the next ten years and the importance of having this view in doing comparative law studies and global financial meditations, and not one student will ever even try to apply these ideas to their work. C'est dommage, what a pity1"
I then said that legal and financial studies are in a quandary because the ambition of both are quite clear, and the honest academic knows quite well that the so-called "theories" in each are not doing their job which is to give a sense of "presentation-invariance structure of theories." [See, Marquis, Jean Pierre (2009) From a Geometric Point of View, at 234.] What does this mean? It means that somehow the idea, and here I must insist on the Platonic concept of idea, simply does not change! It is invariant against all presentations! But this has no meaning at all unless we relax to the nth degree what we mean by equivalence. The clarity coming out of Category Theory is the discovery of a way of showing how we can move from a simple and absolutely intuitive sense of "equals to" as in A = A, to more and more weakened senses of "equivalence," i.e., in order of degrees of weakness, (1) isomorphism, (2) natural transformation, (3) natural isomorphism, (4) adjunction. As we move to weaker and weaker forms of equivalence, we start to realise what we really mean by "identity."
Now, I had prepared mentally for this point in the seminar. I knew that my students would look at me as if I were an alien who may or may not have an evil intent on their immediate future. So, I said, "Look, I've been thinking about this for a while, and I think I have an example which you all can understand about how 'weak equivalence' works in the real world. PARASITES."
At this point, I get a look of embarrassed silence. Some look at me in politeness, others are giving me that "yuk" look. I've got their attention, so I continue:
"You all know how parasites work. You walk barefoot in a beautiful paradise, say Hawaii, and you don't mind walking in puddles. But as your foot enters the puddle, a little screw-shaped parasite enters your heel. It burrows deep, gets into your circulatory system, going round and round your blood system, until it lodges idyllically in your liver or your lungs, and there it grows to an enormous size and proliferates seeds of itself, which then are re-deposited to the environment through your faeces."
They grimace at faeces. They don't like me taking them down THAT path, so I take them up the theoretical track.
"So, look at what's going on here. How is it that such a simple small organism is able to travel and adjust to such exotic and hostile environments? Is it intelligent? Does it have some kind of global navigator? Does it depend on the magnetic or coriolli forces of the sun? No. The parasite has a simple linear instruction set which it can simply follow because the environments which it enters are extraordinarily stable over millions of years. So, imagine you are a parasite and this room is the "heel of a human's foot". Your instruction set says something like, "wiggle like hell" when you come into this environment, and this environment is absolutely stable for millions of years because for millions of years the environments of heels are always the SAME. By the way, this is the kind of IDENTITY that we say we must have in Category Theory. Now what? As a parasite, you burrow to the edge of this environment and you break through to the blood circulatory system. Now this environment has also been the same for millions of years, and your instruction set says, "turn off all flagella and float" and wow, you float and float for a couple circulations -- this is like going round the world in a lifeboat for humans -- until you get to a particular chemical environment that "smells like" a liver or a lung, and then and there, "throw anchor." All of these seemingly complex behaviours are reduced to a instruction set where each element corresponds to a particular stable environment. We have an identity of the parasite moving through identical environments for millions of years. This is an example of how IDENTITY works in a WEAKENED EQUIVALENCE. In other words, the parasite through its life cycle shows us an INVARIANCE of PRESENTATION, it will follow a particular path for itself but it is a path that is merely a presentation of a much more general set of equivalent relations. Remember the parasite behaviours from one level and they look "random" but at another level, they are all connected through equivalences, and taken all together those equivalences are invariant."
I got a bunch of "bug eyes" so, I ended this part of the lecture with, "OK, remember the Parasite."
Parasites: Presentation-Invariance and Degrees of Weakened Equivalence
Last night in the seminar on Legal Aspects of International Finance, we had each student read their draft assignments on various aspects of international financial regulations, e.g., the Orderly Liquidation Authority, Whistleblower Incentives and Protection, OTC derivatives under the Dodd -Frank Act, the EC proposal to regulate the OTC derivatives markets, the Volker Rule under Dodd-Frank and the Vickers Report in the UK.
I said to this small but very able group, "I'll be lecturing on Category Theory for the next ten years and the importance of having this view in doing comparative law studies and global financial meditations, and not one student will ever even try to apply these ideas to their work. C'est dommage, what a pity1"
I then said that legal and financial studies are in a quandary because the ambition of both are quite clear, and the honest academic knows quite well that the so-called "theories" in each are not doing their job which is to give a sense of "presentation-invariance structure of theories." [See, Marquis, Jean Pierre (2009) From a Geometric Point of View, at 234.] What does this mean? It means that somehow the idea, and here I must insist on the Platonic concept of idea, simply does not change! It is invariant against all presentations! But this has no meaning at all unless we relax to the nth degree what we mean by equivalence. The clarity coming out of Category Theory is the discovery of a way of showing how we can move from a simple and absolutely intuitive sense of "equals to" as in A = A, to more and more weakened senses of "equivalence," i.e., in order of degrees of weakness, (1) isomorphism, (2) natural transformation, (3) natural isomorphism, (4) adjunction. As we move to weaker and weaker forms of equivalence, we start to realise what we really mean by "identity."
Now, I had prepared mentally for this point in the seminar. I knew that my students would look at me as if I were an alien who may or may not have an evil intent on their immediate future. So, I said, "Look, I've been thinking about this for a while, and I think I have an example which you all can understand about how 'weak equivalence' works in the real world. PARASITES."
At this point, I get a look of embarrassed silence. Some look at me in politeness, others are giving me that "yuk" look. I've got their attention, so I continue:
"You all know how parasites work. You walk barefoot in a beautiful paradise, say Hawaii, and you don't mind walking in puddles. But as your foot enters the puddle, a little screw-shaped parasite enters your heel. It burrows deep, gets into your circulatory system, going round and round your blood system, until it lodges idyllically in your liver or your lungs, and there it grows to an enormous size and proliferates seeds of itself, which then are re-deposited to the environment through your faeces."
They grimace at faeces. They don't like me taking them down THAT path, so I take them up the theoretical track.
"So, look at what's going on here. How is it that such a simple small organism is able to travel and adjust to such exotic and hostile environments? Is it intelligent? Does it have some kind of global navigator? Does it depend on the magnetic or coriolli forces of the sun? No. The parasite has a simple linear instruction set which it can simply follow because the environments which it enters are extraordinarily stable over millions of years. So, imagine you are a parasite and this room is the "heel of a human's foot". Your instruction set says something like, "wiggle like hell" when you come into this environment, and this environment is absolutely stable for millions of years because for millions of years the environments of heels are always the SAME. By the way, this is the kind of IDENTITY that we say we must have in Category Theory. Now what? As a parasite, you burrow to the edge of this environment and you break through to the blood circulatory system. Now this environment has also been the same for millions of years, and your instruction set says, "turn off all flagella and float" and wow, you float and float for a couple circulations -- this is like going round the world in a lifeboat for humans -- until you get to a particular chemical environment that "smells like" a liver or a lung, and then and there, "throw anchor." All of these seemingly complex behaviours are reduced to a instruction set where each element corresponds to a particular stable environment. We have an identity of the parasite moving through identical environments for millions of years. This is an example of how IDENTITY works in a WEAKENED EQUIVALENCE. In other words, the parasite through its life cycle shows us an INVARIANCE of PRESENTATION, it will follow a particular path for itself but it is a path that is merely a presentation of a much more general set of equivalent relations. Remember the parasite behaviours from one level and they look "random" but at another level, they are all connected through equivalences, and taken all together those equivalences are invariant."
I got a bunch of "bug eyes" so, I ended this part of the lecture with, "OK, remember the Parasite."
Sunday 4 March 2012
Can we go beyond tribal minds?
Can we go beyond the tribal mind?
Thucydides says the preconditions of war are:
(1) colonists (literally, farmers) who set up settlements on other's lands,
(2) bilateral agreements (treaties) of support if one or the other is attacked,
(3) multiple bilateral treaties turn into alliances between members of one group against members of another group, so that
(4) insult, injury or betrayal of one member sets off retaliation but even more importantly,
(5) sussing out and anticipating the consequences of (1) to (4), ANY member looks to other members of an alliance to launch a pre-emptive strike against a member of another alliance. Since membership to an alliance can change by mere threat, a grinding, mutually destructive scenario is primed.
For the great works on war as the reality of the human condition, see:
(a)Thucydides on the History of the Peloponnesian Wars [http://classics.mit.edu/Thucydides/pelopwar.html] and
(b) Gibbon on The History of the Decline and Fall of the Roman Empire [http://www.gutenberg.org/files/25717/25717-h/25717-h.htm].
The great anthropologist Levi-Strauss, after studying tribal wars and classificatory symbolic systems of traditional peoples in South America, use to write: "trade (materials and women) or die." I would say this slogan is somewhat confirmed by Potts' and Hayden's (2008) biological evolutionary thesis in their book, in Sex and Death: How Biology Explains Warfare and Terrorism And Offers a Path to a Safer World.
Thucydides says the preconditions of war are:
(1) colonists (literally, farmers) who set up settlements on other's lands,
(2) bilateral agreements (treaties) of support if one or the other is attacked,
(3) multiple bilateral treaties turn into alliances between members of one group against members of another group, so that
(4) insult, injury or betrayal of one member sets off retaliation but even more importantly,
(5) sussing out and anticipating the consequences of (1) to (4), ANY member looks to other members of an alliance to launch a pre-emptive strike against a member of another alliance. Since membership to an alliance can change by mere threat, a grinding, mutually destructive scenario is primed.
For the great works on war as the reality of the human condition, see:
(a)Thucydides on the History of the Peloponnesian Wars [http://classics.mit.edu/Thucydides/pelopwar.html] and
(b) Gibbon on The History of the Decline and Fall of the Roman Empire [http://www.gutenberg.org/files/25717/25717-h/25717-h.htm].
The great anthropologist Levi-Strauss, after studying tribal wars and classificatory symbolic systems of traditional peoples in South America, use to write: "trade (materials and women) or die." I would say this slogan is somewhat confirmed by Potts' and Hayden's (2008) biological evolutionary thesis in their book, in Sex and Death: How Biology Explains Warfare and Terrorism And Offers a Path to a Safer World.
Friday 2 March 2012
Naive Category Theory is Sufficient to Subsume Asymmetric Bias; Clear the Way to Adjunctions in Law and Finance
1. Today, in my Facebook, I wrote:
An example of "asymmetric bias" is where one group of people feel they are following a correct procedure and therefore, are immune from justice. In the new category theory of law and finance, this is the MISTAKE of confusing translational symmetry (eg procedure) for justice (eg rotational symmetry). An example of this bias can found in the ISDA Determinations Committee view of the "voluntary 70% nonpayment" of bonds as a "non-default." To understand why this determination is actually an asymmetric bias, you might ask yourself, "when has a banker ever treated you as being not in default when you failed to pay 70% of the debt due and payable?" The answer establishes a bilateral symmetry. Now imagine multiplying this question out to all members of society and receiving answers. If the answer is basically the same, then you will have a sense of the rotational symmetry. Biases form part of a transformational group that define the space. With category theory, we can "conceptually calculate" an instantiation of the space that is "presentation-invariant" of the theory. Sounds vague, but it is actually rigorously fun and exciting once you get the hang of it, like skiing. For the latest on the defensiveness of the ISDA determinations committee, see: http://www.zerohedge.com/news/isdas-take-lack-greek-cds-trigger-we-think-credit-eventdc-process-fair-transparent-and-well-tes
2. If you've bothered to follow the argument in this blog re a Category Theory of Law and Finance, you will note that I have tried to show how a few formalism coming from what is now called Category Theory may be applied to: (1) the Arrow-Debreu-Sharpe (ADS) Model of the Financial Contract (FC) can be thought of as the fundamental unit of the law and finance universe with the quadrangle sketch with the four objects t0 ("t zero") for initial conditions, infinite contingent states of the world (Inf-C), Pay, and t1 ("t one") as the "maturity condition" when payment is due and payable. Let's label the morphisms between the objects, f, g, h and i, so that:
f: t0, Inf-C
g: Inf-C, P
h: t1, P
i: t0, t1
It's a lot easier to see what's going on if you draw the morphisms, so it looks like a "square."
Inf-C -------->P
/\ /\
| |
| |
t0----------> t1
3. The above ADS Model is a brilliant reduction of the complex law and finance phenomena since it captures most of the important and significant features of the basic unit of behaviours in the financial markets, including primary (eg, prospectus disclosures under a 1933 Securities Act regime) and secondary (eg, ongoing reporting requirements under a 1934 Securities Exchange Act regime) behaviours. But there is one big issue that it tends to pass over and that is, the phenomenon of Default.
4. Default is a fact of life. In Aristotelian terms, default is at least a "potential-actuality." I would go so far as to assert that its primary substance is commingled with primary matter in the classical sense of undifferentiated matter, where really no distinctions can be made except for that it is an ingredient that makes up the world. This undifferentiated quality links it to Uncertainty, and Uncertainty is basically the same thing as saying "infinite contingent states of the world.". So,in terms of a Category Theory diagram (which uses equinal morphisms) we have:
Default --> Potential-Actuality --> Primary Substance --> The Undifferentiated --> Uncertainty --> Infinite States of the World
5. Default Invariance. I guess my contribution to the Category Theory of Law and Finance is that the ADS Model is insufficient to capture the legal and financial reality. To be even more precise, the ADS Model fails to show the presentation-invariance of the general structure in which financial contracts exist. This is an enormous claim! And it is an example of the philosophical importance of Category Theory in general. So, in order to correct the model so that it is ontologically and epistemologically coherent, we MUST add "not-pay" as a possible alternative object to "pay." Now this change may sound trivial, but it cleaves the universe of possibilities and gives us the "presentation-invariance" that we need for a fundamental unit of legal and financial space. In simpler terms, we can now do conceptual calculations that take account more of the space that constitute legal and financial reality. From this foundation, we can connect to:
(1) Akerloff (1970) where
(a) Part 1 of his paper where information asymmetry favouring the seller leads to market failure is simply the morphism from not-pay and where
(b) Part 2 of his paper where information asymmetry favouring the buyer never leads to market failure corresponds to the morphism from pay [sorry, this thought deserves a simple diagram and a couple thousand words of explanation];
(2) Hohfeld's Legal Conceptions where
(a) Jural Opposites and
(b) Jual Correlatives
form the Category of Legal Relations, which act as a sort for the various legal interpretations of Financial Contracts [again, apologies, this thought deserves an essay unto itself];
(3) Default Invariance implemented into
(a) the Great Cycle of Default which is the four phase mega-states of the world of law and finance (recall previous notes on the definition of Financial Innovation [I] and Bailout [B], where we have the ordered qaudtuple, [I][I], [I][B], [B][B] and [B][I], and where various regulatory proposals can be mapped as morphisms from one phase to another) eg,
(i) the Orderly Liquidation Authority of Title II of the Dodd-Frank Act is a morphism from [I][B] to [B][B], and
(ii) the Whistleblower Incentives Orotection of the Dodd-Frank Act is a morphism from [B][B] to [I][I].
These "regulatory highways" tend to accelerate transitions from one phase to another, AND there are
(4) Opetopes, that is, morphisms on morphisms between these regulatory highways which have a n-category characteristics--I.e., I suppose, at the crazy complex legal and financial level of decision-making, we have the miraculous opetopes (Many-to-One) morphisms.
Ok, got that?
6. To check that we are on the same page, you might try "sketching" all the items stated in paragraph 5 above. There's actually a whole school of Category Theory by C. Ehresmann which developed the concept of esquisse (sketch) that systematically developed sketches as the rigorous syntactics and semantics of the theory. [See, Marquis, Jean-Pierre (2009) p. 225.]
7. Now, we have been using a Naive form of Category Theory, that is, up to isomorphisms of objects where the diagrams commute to at least one "cone.". That is, where we have the objects, A, B and C, we have the following morphisms: f: A->B, g:B->C, and h:A->C, h = gf. But really, where Category Theory proper makes itself fantastically useful is when we can show that we have ADJUNCTIONS.
8. An adjunction, in one simple (but not exact) version, is merely an equivalence of functors between categories. If anyone can show that adjunctions exist in law and finance, then that person or group of people deserve at least one Nobel Prize. At this point in time, I have a couple ideas of why there is no objection to have adjunctions in law and finance systems. But to PROVE the positive of this statement....well, that would be really amazing!
An example of "asymmetric bias" is where one group of people feel they are following a correct procedure and therefore, are immune from justice. In the new category theory of law and finance, this is the MISTAKE of confusing translational symmetry (eg procedure) for justice (eg rotational symmetry). An example of this bias can found in the ISDA Determinations Committee view of the "voluntary 70% nonpayment" of bonds as a "non-default." To understand why this determination is actually an asymmetric bias, you might ask yourself, "when has a banker ever treated you as being not in default when you failed to pay 70% of the debt due and payable?" The answer establishes a bilateral symmetry. Now imagine multiplying this question out to all members of society and receiving answers. If the answer is basically the same, then you will have a sense of the rotational symmetry. Biases form part of a transformational group that define the space. With category theory, we can "conceptually calculate" an instantiation of the space that is "presentation-invariant" of the theory. Sounds vague, but it is actually rigorously fun and exciting once you get the hang of it, like skiing. For the latest on the defensiveness of the ISDA determinations committee, see: http://www.zerohedge.com/news/isdas-take-lack-greek-cds-trigger-we-think-credit-eventdc-process-fair-transparent-and-well-tes
2. If you've bothered to follow the argument in this blog re a Category Theory of Law and Finance, you will note that I have tried to show how a few formalism coming from what is now called Category Theory may be applied to: (1) the Arrow-Debreu-Sharpe (ADS) Model of the Financial Contract (FC) can be thought of as the fundamental unit of the law and finance universe with the quadrangle sketch with the four objects t0 ("t zero") for initial conditions, infinite contingent states of the world (Inf-C), Pay, and t1 ("t one") as the "maturity condition" when payment is due and payable. Let's label the morphisms between the objects, f, g, h and i, so that:
f: t0, Inf-C
g: Inf-C, P
h: t1, P
i: t0, t1
It's a lot easier to see what's going on if you draw the morphisms, so it looks like a "square."
Inf-C -------->P
/\ /\
| |
| |
t0----------> t1
3. The above ADS Model is a brilliant reduction of the complex law and finance phenomena since it captures most of the important and significant features of the basic unit of behaviours in the financial markets, including primary (eg, prospectus disclosures under a 1933 Securities Act regime) and secondary (eg, ongoing reporting requirements under a 1934 Securities Exchange Act regime) behaviours. But there is one big issue that it tends to pass over and that is, the phenomenon of Default.
4. Default is a fact of life. In Aristotelian terms, default is at least a "potential-actuality." I would go so far as to assert that its primary substance is commingled with primary matter in the classical sense of undifferentiated matter, where really no distinctions can be made except for that it is an ingredient that makes up the world. This undifferentiated quality links it to Uncertainty, and Uncertainty is basically the same thing as saying "infinite contingent states of the world.". So,in terms of a Category Theory diagram (which uses equinal morphisms) we have:
Default --> Potential-Actuality --> Primary Substance --> The Undifferentiated --> Uncertainty --> Infinite States of the World
5. Default Invariance. I guess my contribution to the Category Theory of Law and Finance is that the ADS Model is insufficient to capture the legal and financial reality. To be even more precise, the ADS Model fails to show the presentation-invariance of the general structure in which financial contracts exist. This is an enormous claim! And it is an example of the philosophical importance of Category Theory in general. So, in order to correct the model so that it is ontologically and epistemologically coherent, we MUST add "not-pay" as a possible alternative object to "pay." Now this change may sound trivial, but it cleaves the universe of possibilities and gives us the "presentation-invariance" that we need for a fundamental unit of legal and financial space. In simpler terms, we can now do conceptual calculations that take account more of the space that constitute legal and financial reality. From this foundation, we can connect to:
(1) Akerloff (1970) where
(a) Part 1 of his paper where information asymmetry favouring the seller leads to market failure is simply the morphism from not-pay and where
(b) Part 2 of his paper where information asymmetry favouring the buyer never leads to market failure corresponds to the morphism from pay [sorry, this thought deserves a simple diagram and a couple thousand words of explanation];
(2) Hohfeld's Legal Conceptions where
(a) Jural Opposites and
(b) Jual Correlatives
form the Category of Legal Relations, which act as a sort for the various legal interpretations of Financial Contracts [again, apologies, this thought deserves an essay unto itself];
(3) Default Invariance implemented into
(a) the Great Cycle of Default which is the four phase mega-states of the world of law and finance (recall previous notes on the definition of Financial Innovation [I] and Bailout [B], where we have the ordered qaudtuple, [I][I], [I][B], [B][B] and [B][I], and where various regulatory proposals can be mapped as morphisms from one phase to another) eg,
(i) the Orderly Liquidation Authority of Title II of the Dodd-Frank Act is a morphism from [I][B] to [B][B], and
(ii) the Whistleblower Incentives Orotection of the Dodd-Frank Act is a morphism from [B][B] to [I][I].
These "regulatory highways" tend to accelerate transitions from one phase to another, AND there are
(4) Opetopes, that is, morphisms on morphisms between these regulatory highways which have a n-category characteristics--I.e., I suppose, at the crazy complex legal and financial level of decision-making, we have the miraculous opetopes (Many-to-One) morphisms.
Ok, got that?
6. To check that we are on the same page, you might try "sketching" all the items stated in paragraph 5 above. There's actually a whole school of Category Theory by C. Ehresmann which developed the concept of esquisse (sketch) that systematically developed sketches as the rigorous syntactics and semantics of the theory. [See, Marquis, Jean-Pierre (2009) p. 225.]
7. Now, we have been using a Naive form of Category Theory, that is, up to isomorphisms of objects where the diagrams commute to at least one "cone.". That is, where we have the objects, A, B and C, we have the following morphisms: f: A->B, g:B->C, and h:A->C, h = gf. But really, where Category Theory proper makes itself fantastically useful is when we can show that we have ADJUNCTIONS.
8. An adjunction, in one simple (but not exact) version, is merely an equivalence of functors between categories. If anyone can show that adjunctions exist in law and finance, then that person or group of people deserve at least one Nobel Prize. At this point in time, I have a couple ideas of why there is no objection to have adjunctions in law and finance systems. But to PROVE the positive of this statement....well, that would be really amazing!
Wednesday 15 February 2012
Civilisation and Its Class-A Discontents: 97th Session of The Philosophical Foundations of Law and Finance
Title: Civilisation and Its Class-A Discontents
Date: February 17, 2012
Time: 6 to 8pm
Venue: room 516, 319 Regent Street, University of Westminster
Dinner: Thai or Persian or Just Drinks Depending
Le Menu
For the 97th Session of the Philosophical Foundations of Law and Finance, we will examine the quasi-Freudian concept of CIVILISATION AND ITS DISCONTENTS through three and a half lenses:
(1) The Myth of the High Flyer
(a) Please play and meditate on the morphisms, functors and categories implied by: http://www.youtube.com/watch?v=D6REtT0B1VA&feature=youtube_gdata_player)
(2) The Myth of Financialisation via Securitization
(a) Kettering, K.C. (2008) Securitization and Its Discontents, The Dynamics of Financial Product Development, at: http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1012937
(b) Went, P. (2011) Securitization and Its Discontents, at: http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1888410
(3) The Myth of Western Civilisation via The Koan of Bafflement
(a) Denuding the Delusions of Complexification, see Jon Jandai (3 August 2011) Life is Easy, at: http://www.youtube.com/watch?v=21j_OCNLuYg&feature=youtube_gdata_player
(3.5) The Half-Myth of Socialism
(a) On the homotopy of socialism or why socialists such as President Obama believe Hopium Overrides Arithmetic, see: http://www.zerohedge.com/news/biderman-beyond-baffled-bos-budget
After this opetopic journey (the combining of the many into the One), we will adjourn to a nearby restaurant for a meal and some refreshments.
ciao
joe
Date: February 17, 2012
Time: 6 to 8pm
Venue: room 516, 319 Regent Street, University of Westminster
Dinner: Thai or Persian or Just Drinks Depending
Le Menu
For the 97th Session of the Philosophical Foundations of Law and Finance, we will examine the quasi-Freudian concept of CIVILISATION AND ITS DISCONTENTS through three and a half lenses:
(1) The Myth of the High Flyer
(a) Please play and meditate on the morphisms, functors and categories implied by: http://www.youtube.com/watch?v=D6REtT0B1VA&feature=youtube_gdata_player)
(2) The Myth of Financialisation via Securitization
(a) Kettering, K.C. (2008) Securitization and Its Discontents, The Dynamics of Financial Product Development, at: http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1012937
(b) Went, P. (2011) Securitization and Its Discontents, at: http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1888410
(3) The Myth of Western Civilisation via The Koan of Bafflement
(a) Denuding the Delusions of Complexification, see Jon Jandai (3 August 2011) Life is Easy, at: http://www.youtube.com/watch?v=21j_OCNLuYg&feature=youtube_gdata_player
(3.5) The Half-Myth of Socialism
(a) On the homotopy of socialism or why socialists such as President Obama believe Hopium Overrides Arithmetic, see: http://www.zerohedge.com/news/biderman-beyond-baffled-bos-budget
After this opetopic journey (the combining of the many into the One), we will adjourn to a nearby restaurant for a meal and some refreshments.
ciao
joe
Friday 20 January 2012
Market Morphisms: Pump, Chase, Game and Crush
In every "Market," we have the following ordered morphisms: pump, chase, game, crush. The pumpers are the fraudsters (think of hopium addicts of IPOs and the corporate suits posing as newspersons), the chasers are the ignorant hypnotically susceptible masses (guru devotees, Obama groupies, retail investors and now the new institutional investors), the gamesters are the High Frequency Trading robots (trading at the speed of DARKNESS and taking the mickey out of the chasers), and finally the BONE CRUSHERS (today, this role is played by our Central Bankers, but in the historical record, these were the pinnacle ontogenetic-phyllogenic exemplars of the "killer-same-species" Y-chromosome gene e.g. Ghenghis Khan, King Niall, Nurhaci or was it Giocangga?, King Solomon, President Kennedy. etc.) Our faith in the ATMs working today is in the CB bone crushers and they can't help being what they are. Take care, you all!
Thursday 5 January 2012
DEFAULT INVARIANCE: Announcement of New Theory of Law and Finance
120105
For the 95th session of the Philosophical Foundations of Law and Finance, I will read from my unexpurgated and unpublished paper entitled, "Default Invariance." The thesis is that the intersecting discourses of law and finance, normally associated with the professional discourse of risk, can be translated into an UNIVERSAL ALGEBRA, {D, *}, where D stands for "human decisions" and * stands for any one of three isomorphisms, bilateral, translational or rotational. Beauty is thus a result of fundamental binary operations and incorporated into the firey belly of the equations. Since decisions are the objects and the three symmetries are the isomorphisms, the theory logically anticipates and therefore generously incorporates the traditional micro- to macro- economic equilibrium premises of Morgenstein, Von Neumann, Tversky, Kahneman, Debreu, Arrow. To illustrate this algebraic approach to law and finance, we critically examine the Arrow-Debreu-Sharpe model (1995) of a financial contract -- where Time 0 (T0) conditions point to an infinitely contingent states of the world and T1 points to the event of "pay". Theorists using ADS premises have an extremely biased view of financial contracts and have led to over-confidence and over-reliance in the prediction of pay events. For example, such theorists wrongly impute the value "1" for "payment" and "0" for "nonpayment." We correct this model by injecting the symmetric resultants of "pay or not-pay" to the interval between t0 and t1. What follows naturally is what is termed DEFAULT INVARIANCE. Thus, the values of "pay" and "not-pay" must be "0" and "1", respectively. This result has extraordinarily large implications for law and finance theory. For example, from this theory, a financial contract when paid exits from the infinitely contingent states of the world, i.e., (infinite-contingency) x 0 = 0, and thus, becomes a legal certainty of discharged obligations. And if unpaid, it remains as part of the infinitely contingent states of the world, i.e., (infinite contingency) x 1 = infinite contingency, and a continuing potential legal liability. One implication of this new theory is that another type of credit rating must exist in the real world (whether we like it or not). The current credit ratings in the world are based on the question of whether a legal entity can make good its financial obligations at T1. This is obviously based on an Arrow-Debreu model which sees "pay" as the only relevant event at T1. From this premise, the hierarchy of ratings AAA, AA, and so on unfolds. But this sort of credit rating obviously does not capture the continuing ("stretched out") event of non-payment except to nominate it at the bottom of ratings. From a "not-pay" event, an alternative credit rating agency would appropriate "XXX" to warn potential investors of the severity or intensity of default. (Think of warning labels on videos that are not appropriate to non-adults.) Some might argue that the XXX-rating is already incorporated in the AAA-rating system. But it is patently not since during times of credit crises, large institutional short-term traders asses the risk of AAA-instruments as "100% default probability."
For the 95th session of the Philosophical Foundations of Law and Finance, I will read from my unexpurgated and unpublished paper entitled, "Default Invariance." The thesis is that the intersecting discourses of law and finance, normally associated with the professional discourse of risk, can be translated into an UNIVERSAL ALGEBRA, {D, *}, where D stands for "human decisions" and * stands for any one of three isomorphisms, bilateral, translational or rotational. Beauty is thus a result of fundamental binary operations and incorporated into the firey belly of the equations. Since decisions are the objects and the three symmetries are the isomorphisms, the theory logically anticipates and therefore generously incorporates the traditional micro- to macro- economic equilibrium premises of Morgenstein, Von Neumann, Tversky, Kahneman, Debreu, Arrow. To illustrate this algebraic approach to law and finance, we critically examine the Arrow-Debreu-Sharpe model (1995) of a financial contract -- where Time 0 (T0) conditions point to an infinitely contingent states of the world and T1 points to the event of "pay". Theorists using ADS premises have an extremely biased view of financial contracts and have led to over-confidence and over-reliance in the prediction of pay events. For example, such theorists wrongly impute the value "1" for "payment" and "0" for "nonpayment." We correct this model by injecting the symmetric resultants of "pay or not-pay" to the interval between t0 and t1. What follows naturally is what is termed DEFAULT INVARIANCE. Thus, the values of "pay" and "not-pay" must be "0" and "1", respectively. This result has extraordinarily large implications for law and finance theory. For example, from this theory, a financial contract when paid exits from the infinitely contingent states of the world, i.e., (infinite-contingency) x 0 = 0, and thus, becomes a legal certainty of discharged obligations. And if unpaid, it remains as part of the infinitely contingent states of the world, i.e., (infinite contingency) x 1 = infinite contingency, and a continuing potential legal liability. One implication of this new theory is that another type of credit rating must exist in the real world (whether we like it or not). The current credit ratings in the world are based on the question of whether a legal entity can make good its financial obligations at T1. This is obviously based on an Arrow-Debreu model which sees "pay" as the only relevant event at T1. From this premise, the hierarchy of ratings AAA, AA, and so on unfolds. But this sort of credit rating obviously does not capture the continuing ("stretched out") event of non-payment except to nominate it at the bottom of ratings. From a "not-pay" event, an alternative credit rating agency would appropriate "XXX" to warn potential investors of the severity or intensity of default. (Think of warning labels on videos that are not appropriate to non-adults.) Some might argue that the XXX-rating is already incorporated in the AAA-rating system. But it is patently not since during times of credit crises, large institutional short-term traders asses the risk of AAA-instruments as "100% default probability."
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