文章基本信息

标题：Game-Theoretic Derivation of Discrete Distributions and Discrete Pricing Formulas
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作者：Akimichi Takemura ; Taiji Suzuki
期刊名称：JOURNAL OF THE JAPAN STATISTICAL SOCIETY
印刷版ISSN：1882-2754
电子版ISSN：1348-6365
出版年度：2007
卷号：37
期号：1
页码：87-104
DOI：10.14490/jjss.37.87
出版社：JAPAN STATISTICAL SOCIETY
摘要：In this expository paper, we illustrate the generality of the 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 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 binomial tree models. However the game-theoretic framework is advantageous because it eliminates the need for any a priori probabilistic assumption.
关键词：binomial distribution;Cox-Ross-Rubinstein formula;hypergeometric distribution;lower price;Polya's distribution;probability protocol;replicating strategy;upper price