ゲーム論的確率論の予測理論への応用

基于博弈的概率论在预测理论中的应用

• 批准号: 18650070
• 负责人: 竹村 彰通
• 金额: $ 1.98万
• 依托单位: The University of Tokyo
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Exploratory Research
• 财政年份: 2006
• 资助国家: 日本
• 起止时间: 2006 至 2008
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-18650070/
• 关键词: 大数の強法則; 重複対数の法則; 中心極限定理

Vladimir VovkとGlenn Shafer によるゲーム論的確率論は以下の著書でその基礎が与えられた.Glenn Shafer and Vladimir Vovk. Probability and Finance:It's Only a Game! Wiley, New York, 2001そこでは,Skepticとよばれる賭をする人と,Realityとよばれる賭の結果を定める人の,二人のプレーヤーの間のゲームを設定することにより,ゲームの結果として確率が定まることが示されている.注目すべきは,測度論無しに,大数の強法則,中心極限定理,重複対数の法則,さらに数理ファイナンスにおける価格付けの諸公式,などが証明される点にある.竹村は,竹内啓,公文雅之との共同研究を通じて,ゲーム論的確率論に関する新たな結果を得ている.これらはtechnical reportとして発表されていたが,研究発表に示すように国際雑誌に刊行の段階となっている.また竹村はShafer氏およびVovk氏とも共同研究を進めており,以下の研究成果を得た."The game-theoretic martingales behind the zero-one laws", by Akimichi Takemura, Vladimir Vovk and Glenn Shafer. Techinical Report METR 08-18, March 2008.この研究では,測度論の諸仮定をおくことなく,コルモゴロフの0-1法則などの0-1法則の一般的な形をゲーム論的枠組で示している.

Vladimir Vovk and Glenn Shafer are the authors of the book.Glenn Shafer and Vladimir Vovk. Probability and Finance:It's Only a Game! Wiley, New York, 2001 "Skeptic,Reality, and Results of Gambling". Note that, measure theory, the strong law of large numbers, the central limit theorem, the law of repeated pairs, mathematical formulas, proofs, etc. Takemura, Takeuchi, and Kumon Masayuki jointly studied the new results of the study. This is a technical report and a research report published in international journals. Shafer's and Vovk's joint research has been carried out, and the following research results have been obtained. "The game-theoretic martingales behind the zero-one laws", by Akimichi Takemura, Vladimir Vovk and Glenn Shafer. Technical Report METR 08-18, March 2008. This research is aimed at the determination of the 0 -1 rule of measurement theory and the general form of the 0 - 1 rule of measurement theory.

项目成果

Capital process and optimality properties of a Bayesian skeptic in coin-tossing games

抛硬币游戏中贝叶斯怀疑论者的资本过程和最优性属性

• 发表时间: 2008
• 期刊: Stochastic Analysis and Applications 26
• 作者: Masayuki Kumon;A. Takemura and Kei Takeuchi
• 通讯作者: A. Takemura and Kei Takeuchi

Game-theoretic derivation of discrete distributions and discrete pricing formulas

离散分布和离散定价公式的博弈论推导

• 发表时间: 2007
• 期刊: Journal of the Japan Statistical Society 37
• 作者: 沼田秀穂;福田豊;Akimichi Takemura and Taiji Suzuki
• 通讯作者: Akimichi Takemura and Taiji Suzuki

On a simple strategy weakly forcing the storong law of large numbers in the bounded forecasting game.

在有界预测游戏中弱强制大数定律的简单策略。

• 发表时间: 2008
• 期刊: Annals of the Institute of Statistical Mathematics, 60
• 作者: Masayuki Kumon;A. Takemura and Kei Takeuchi;Yasunori Horikoshi and A. Takemura.;Masayuki Kumon and A. Takemura
• 通讯作者: Masayuki Kumon and A. Takemura

Game-theoretic versions of strong law of large numbers for unbounded variables

无界变量的强大数定律的博弈论版本

• 发表时间: 2007
• 期刊: Stochastics 79
• 作者: Masayuki Kumon;Akimichi Takemura and Kei Takeuchi
• 通讯作者: Akimichi Takemura and Kei Takeuchi

Implications of contrarian and one-sided strategies for the fair-coin game

逆向和片面策略对公平硬币游戏的影响

• 发表时间: 2008
• 期刊: Stochastic Processes and their applications (in press)
• 作者: Horikoshi;Y.and Takemura;A.
• 通讯作者: A.