Game theoretic derivation of discrete distributions and discrete pricing formulas

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dc.creatorTakemura, Akimichi
dc.creatorSuzuki, Taiji
dc.date2005-09-16
dc.date.accessioned2026-07-07T12:07:16Z
dc.date.available2026-07-07T12:07:16Z
dc.descriptionIn 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.
dc.identifierhttps://arxiv.org/abs/math/0509367
dc.identifierhttp://arxiv.org/abs/math/0509367
dc.identifierJ. Japan Statist. Soc., Vol.37, No.1, 2007, 87-104
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/208913
dc.subjectProbability
dc.subjectStatistics Theory
dc.subjectTrading and Market Microstructure
dc.titleGame theoretic derivation of discrete distributions and discrete pricing formulas
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