Game theoretic derivation of discrete distributions and discrete pricing formulas

Details Game theoretic derivation of discrete distributions and discrete pricing formulas Game theoretic derivation of discrete distributions and discrete pricing formulas

2005-09-16

arxiv.org/abs/math/0509367v1

J. Japan Statist. Soc., Vol.37, No.1, 2007, 87-104

Mathematics

Probability

Scientific paper

In this expository paper we illustrate the generality of game theoretic probability protocols of Shafer and Vovk (2001) in finite-horizon discrete games. By restricting ourselves to finite-horizon discrete games, we can explicitly describe how discrete distributions with finite support and the discrete pricing formulas, such as the Cox-Ross-Rubinstein formula, are naturally derived from game-theoretic probability protocols. Corresponding to any discrete distribution with finite support, we construct a finite-horizon 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.

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