Game-theoretic probability and its applications in finance

Abstract

Game-theoretic probability is an old alternative to the standard measure-theoretic probability theory. The main difference between the two approaches to probability is that the notion of game-theoretic probability is derivative: it is defined via other more fundamental notions (for example, via the security prices in the context of financial markets). This makes it possible to apply the theory of game-theoretic probability in absence of any stochastic assumptions. In the first part of the talk I will review the history of and recent work on game-theoretic probability, and in the second part I will describe some applications to idealized financial markets.In my talk I plan to review results obtained in several papers and in the book by Glenn Shafer and Vladimir Vovk. "Probability and Finance: It's Only a Game!" Wiley, New York, 2001.