The primer on arbitrage conceptions in economics: their logistics, roots and some formal models (historical and bibliographical notes) - Rybicki, Wojciech (Wydawnictwo Uniwersytetu Ekonomicznego we Wrocławiu, 2011)
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”.
Mathematical Economics, 2011, Nr 7 (14), s. 173-197
Keywords: arbitrage; Walrasian law of one price; cournot's exchange cycle; free lunch; linear pricing; martingale; cornucopia