Study of prediction theory based on game-theoretic probability

基于博弈概率的预测理论研究

• 批准号: 22650057
• 负责人: TAKEMURA Akimichi
• 金额: $ 2.14万
• 依托单位: The University of Tokyo
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Challenging Exploratory Research
• 财政年份: 2010
• 资助国家: 日本
• 起止时间: 2010 至 2012
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-22650057/
• 关键词: 統計的予測・制御; ゲーム論的確率論; 確率予測; 重複対数の法則; ロジスティック回帰; 多変量解析; 分類・パタン認識; 計算機集約的統計; 大数法則; 中心極限定理; マルチンゲール; 数理ファイナンス

The game-theoretic probability initiated by Shafer and Vovk reconstructs the probability theory based only on protocols of games. In this study we obtained many results in this framework, such as reconstruction of pricing theory in multinomial games, probability forecasting based on regression, and new sufficient condition for the law of iterated logarithm.

Shafer和Vovk发起的游戏理论概率仅根据游戏协议重建概率理论。在这项研究中，我们在此框架中获得了许多结果，例如在多项式游戏中重建定价理论，基于回归的概率预测以及针对迭代对数定律的新条件。

项目成果

Multistep Bayesian strategy in coin-tossing gamesand its application to asset trading gamesin continuous time

抛硬币游戏中的多步贝叶斯策略及其在连续时间资产交易游戏中的应用

• 发表时间: 2010
• 期刊: Stochastic Analysisand Applications
• 作者: Kei Takeuchi; Masayuki Kumon andAkimichi Takemura
• 通讯作者: Masayuki Kumon andAkimichi Takemura

Convergence of random series and the rate of convergence of the strong law of large numbers in game-theoretic probability

博弈论概率中随机级数的收敛性和大数强定律的收敛率

• DOI: 10.1016/j.spa.2011.10.011
• 发表时间: 2012
• 期刊: Stochastic Processes and their Applications
• 影响因子: 1.4
• 作者: Miyabe;K. and Takemura;A.
• 通讯作者: A.

Multistep Bayesian strategy in coin-tossing games and its application to asset trading games in continuous time.

抛硬币游戏中的多步贝叶斯策略及其在连续时间资产交易游戏中的应用

• 发表时间: 2010
• 期刊: Stochastic Analysis and Applications
• 影响因子: 1.3
• 作者: Kei Takeuchi;Masayuki Kumon;A.Takemura
• 通讯作者: A.Takemura

Levy's zero-one law in game-theoretic probability

博弈论概率中的利维零一定律

• DOI: 10.1007/s10959-011-0390-3
• 发表时间: 2012
• 期刊: Journal of Theoretical Probability
• 影响因子: 0.8
• 作者: Shafer;G.;Vovk;V. and Takemura;A.
• 通讯作者: A.

Approximations and asymptotics of upper hedging prices in multinomial models

多项模型中套期保值上限价格的近似和渐近

• DOI: 10.1007/s13160-011-0047-8
• 发表时间: 2012
• 期刊: Japan Journal of Industrial and Applied Mathematics
• 影响因子: 0.9
• 作者: Nakajima;R.;Kumon;M.;Takemura;A. and Takeuchi;K.
• 通讯作者: K.