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Game theoretic derivation of discrete distributions and discrete pricing formulas

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  • Akimichi Takemura
  • Taiji Suzuki

Abstract

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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  • Akimichi Takemura & Taiji Suzuki, 2005. "Game theoretic derivation of discrete distributions and discrete pricing formulas," Papers math/0509367, arXiv.org.
    • Handle: RePEc:arx:papers:math/0509367
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    References listed on IDEAS

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    1. Cox, John C. & Ross, Stephen A. & Rubinstein, Mark, 1979. "Option pricing: A simplified approach," Journal of Financial Economics, Elsevier, vol. 7(3), pages 229-263, September.
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    Cited by:

    1. Masayuki Kumon & Akimichi Takemura, 2008. "On a simple strategy weakly forcing the strong law of large numbers in the bounded forecasting game," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 60(4), pages 801-812, December.

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