Game-Theoretic Derivation of Discrete Distributions and Discrete Pricing Formulas
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- Takemura Akimichi
- Department of Mathematical Informatics, Graduate School of Information Science and Technology, University of Tokyo
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- Suzuki Taiji
- Department of Mathematical Informatics, Graduate School of Information Science and Technology, University of Tokyo
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説明
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.
収録刊行物
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- JOURNAL OF THE JAPAN STATISTICAL SOCIETY
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JOURNAL OF THE JAPAN STATISTICAL SOCIETY 37 (1), 87-104, 2007
日本統計学会
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詳細情報 詳細情報について
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- CRID
- 1390001205287786624
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- NII論文ID
- 110006317398
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- NII書誌ID
- AA1105098X
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- ISSN
- 13486365
- 18822754
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- NDL書誌ID
- 9304145
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- 本文言語コード
- en
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- データソース種別
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- JaLC
- NDL
- Crossref
- CiNii Articles
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- 使用不可