Game theoretic derivation of discrete distributions and discrete pricing formulas
Abstract
In this expository paper we illustrate the generality of game theoretic probability protocols of Shafer and Vovk (2001) in finitehorizon discrete games. By restricting ourselves to finitehorizon discrete games, we can explicitly describe how discrete distributions with finite support and the discrete pricing formulas, such as the CoxRossRubinstein formula, are naturally derived from gametheoretic probability protocols. Corresponding to any discrete distribution with finite support, we construct a finitehorizon discrete game, a replicating strategy of Skeptic, and a neutral forecasting strategy of Forecaster, such that the discrete distribution is derived from the game. Construction of a replicating strategy is the same as in the standard arbitrage arguments of pricing European options in the binomial tree models. However the game theoretic framework is advantageous because no a priori probabilistic assumption is needed.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 September 2005
 DOI:
 10.48550/arXiv.math/0509367
 arXiv:
 arXiv:math/0509367
 Bibcode:
 2005math......9367T
 Keywords:

 Mathematics  Probability;
 Mathematics  Statistics;
 Quantitative Finance  Trading and Market Microstructure
 EPrint:
 J. Japan Statist. Soc., Vol.37, No.1, 2007, 87104