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  1. 2 Rybicki W.

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The primer on arbitrage conceptions in economics: their logics, roots and some formal models (historical and bibliographical notes)

100%
Rybicki W.
Mathematical Economics
|
2011
|
issue 7 (14)
173-197
EN
The paper makes up the first part of a larger study devoted to arbitrage ideas, models and pricing methodology in spirit of “no arbitrage” (or fairness or transparency) demands.The work – as a whole – is entitled “Arbitrage in Economics and Elsewhere – Facts Well Known and Less Known” and consists of three papers. In the present essay we intentionally interweave “loose (informal) variations on themes” (of arbitrage theories, their applications and connotations) with (brief) demonstrations of selected formal models and some more rigorous mathematical technicalities. Some efforts are made to highlight significant economic aspects as well as to reveal a piece of mathematical “machinery” hidden behind the stories told. Nevertheless, the introductory character of the current paper causes the descriptive, philosophical and historical elements to prevail: we invoke very old roots such as Aristotle‟s or Aquinata‟s thoughts and then follow Cournot, Walras and Keynes works, up to the crucial paper of Miller, Modigliani. Along the way the very deep considerations on the coherency of subjective probability systems are mentioned – “the probabilistic core” of an arbitrage/no arbitrage questions (thoughts of Ramsey and de Finetti). Subsequently, the basics (finite state-space) of the modern, martingale (no arbitrage) modeling (originated by Harrison, Kreps, Pliska) is presented, as well as the “factor-type” schema of the arbitrage pricing theorem (Ross‟s conception). The role played by the supplemented bibliography should be also pointed out. It significantly enters the planned communication. The author‟s aim was to provide the (selected) basis, and “vocabulary” which will be useful for reading the entirety of the “trilogy” – the presented foreword really constitutes a kind of “a bibliographical note”.
2

Arbitrage in economics and elsewhere – facts well known and less known (three papers on arbitrage ideas, modeling and pricing – yesterday, today and tomorrow) – introduction to the series

100%
Rybicki W.
Mathematical Economics
|
2011
|
issue 7 (14)
169-172
XX
The presented series of articles on arbitrage theories and their methodological aspects consist of three papers entitled as follows: I. The Primer on Arbitrage Conceptions in Economics: Their Logics, Roots and Some Formal Models (Historical and Bibliographical Notes). II. Mathematics of Financial Arbitrage: From Algebraic Geometry at the Turn of the 19th and 20th Centuries to Modern Martingale (Generalized) Considerations III. The Arbitrage in Stochastic Finance, Social Choice Theory and Macroeconomics. The articles are devoted to present – in a historical perspective – the basic ideas and “metamorphoses” of the notion and role of an arbitrage (originated as a kind of clever and rational speculation – the last word is used in a “neutral”, not pejorative sense) as well as to point out its various, important connotations (not merely in finance or even economics) and to demonstrate some mathematical inevitable technicalities, reflecting, in fact, the logical essence and the modern view of the arbitrage (and non arbitrage) conditions.
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