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Study of prediction theory based on game-theoretic probability

Research Project

Project/Area Number 22650057
Research Category

Grant-in-Aid for Challenging Exploratory Research

Allocation TypeSingle-year Grants
Research Field Statistical science
Research InstitutionThe University of Tokyo

Principal Investigator

TAKEMURA Akimichi  東京大学, 大学院・情報理工学系研究科, 教授 (10171670)

Project Period (FY) 2010 – 2012
Project Status Completed (Fiscal Year 2012)
Budget Amount *help
¥3,340,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥540,000)
Fiscal Year 2012: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2011: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2010: ¥1,000,000 (Direct Cost: ¥1,000,000)
Keywords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
Research Abstract

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.

Report

(4 results)
  • 2012 Annual Research Report   Final Research Report ( PDF )
  • 2011 Annual Research Report
  • 2010 Annual Research Report
  • Research Products

    (29 results)

All 2013 2012 2011 2010 Other

All Journal Article (16 results) (of which Peer Reviewed: 16 results) Presentation (10 results) (of which Invited: 1 results) Remarks (3 results)

  • [Journal Article] The law of the iterated logarithmin game-theoretic probability withquadratic and stronger hedges、2013

    • Author(s)
      Kenshi Miyabe and Akimichi Takemura
    • Journal Title

      Stochastic Processes and their Applications

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Bayesian logistic betting strategagainst probability forecasting2013

    • Author(s)
      Masayuki Kimono、 Jing Li、 AkimichiTakemura and Kei Takeuchi
    • Journal Title

      Stochastic Analysis and Applications

      Volume: 31 Pages: 214-234

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Bayesian logistic betting strategy against probability forecasting.2013

    • Author(s)
      Masayuki Kumon, Jing Li, A.Takemura and Kei Takeuchi.
    • Journal Title

      Stochastic Analysis and Applications

      Volume: 31 Pages: 214-234

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The law of the iterated logarithm in game-theoretic probability with quadratic and stronger hedges2013

    • Author(s)
      K. Miyabe and A. Takemura
    • Journal Title

      Stochastic Preocesses and their Applications

      Volume: 123 Issue: 8 Pages: 3132-3152

    • DOI

      10.1016/j.spa.2013.03.018

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Levy's zero-one law in game-theoretic probability2012

    • Author(s)
      Shafer, G., Vovk, V. and Takemura, A.
    • Journal Title

      Journal of Theoretical Probability

      Volume: VOL.25 Issue: 1 Pages: 1-24

    • DOI

      10.1007/s10959-011-0390-3

    • Related Report
      2012 Final Research Report 2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Approximations and asymptotics of upperhedging prices in multinomial models2012

    • Author(s)
      Ryuichi Nakajima、 Masayuki Kumon、Akimichi Takemura and Kei Takeuchi、
    • Journal Title

      Japan Journal of Industrial and Applied Mathematics

      Volume: 25 Pages: 1-21

    • NAID

      10030213864

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Approximations and asymptotics of upper hedging prices in multinomial models.2012

    • Author(s)
      Ryuichi Nakajima, Masayuki Kumon, A.Takemura and Kei Takeuchi.
    • Journal Title

      Japan Journal of Industrial and Applied Mathematics

      Volume: 25 Pages: 1-21

    • NAID

      10030213864

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Convergence of random series and the rate of convergence of the strong law of large numbers in game-theoretic probability.2012

    • Author(s)
      Kenshi Miyabe and A.Takemura.
    • Journal Title

      Stochastic Processes and their Applications

      Volume: 122 Pages: 1-30

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Approximations and asymptotics of upper hedging prices in multinomial models2012

    • Author(s)
      Nakajima, R., Kumon, M., Takemura, A. and Takeuchi, K.
    • Journal Title

      Japan Journal of Industrial and Applied Mathematics

      Volume: VOL.25 Issue: 1 Pages: 1-21

    • DOI

      10.1007/s13160-011-0047-8

    • NAID

      10030213864

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Convergence of random series and the rate of convergence of the strong law of large numbers in game-theoretic probability2012

    • Author(s)
      Miyabe, K. and Takemura, A.
    • Journal Title

      Stochastic Processes and their Applications

      Volume: VOL.122 Issue: 1 Pages: 1-30

    • DOI

      10.1016/j.spa.2011.10.011

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Sequentialoptimizing strategy in multi-dimensionalbounded forecasting games、 Stochastic2011

    • Author(s)
      Masayuki Kumon、 Akimichi Takemura andKei Takeuchi
    • Journal Title

      Processes and their Applications

      Volume: 121 Pages: 155-183

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Sequential optimizing strategy in multi-dimensional bounded forecasting games.2011

    • Author(s)
      Masayuki Kumon, A. Takemuraand Kei Takeuchi
    • Journal Title

      Stochastic Processes and their Applications

      Volume: 121 Pages: 155-183

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Multistep Bayesian strategy in coin-tossing gamesand its application to asset trading gamesin continuous time2010

    • Author(s)
      Kei Takeuchi、 Masayuki Kumon andAkimichi Takemura
    • Journal Title

      Stochastic Analysisand Applications

      Volume: 28 Pages: 842-861

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] New procedures fortesting whether stock price processes aremartingales2010

    • Author(s)
      Kei Takeuchi、 Akimichi Takemura andMasayuki Kumon
    • Journal Title

      Computational Economics

      Volume: 37 Pages: 67-88

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Multistep Bayesian strategy in coin-tossing games and its application to asset trading games in continuous time.2010

    • Author(s)
      Kei Takeuchi, Masayuki Kumon, A.Takemura
    • Journal Title

      Stochastic Analysis and Applications

      Volume: 28 Pages: 842-861

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] New procedures for testing whether stock price processes are martingales.2010

    • Author(s)
      Kei Takeuchi, A.Takemura, Masayuki Kumon
    • Journal Title

      Computational Economics

      Volume: 37 Pages: 67-88

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Presentation] 独立分布でない場合の大数の法則の収束測度-ゲーム論的確率論からのアプローチ-、2012

    • Author(s)
      宮部 賢志・竹村 彰通
    • Organizer
      2012日本数学会
    • Place of Presentation
      東京理科大学 神楽坂キャンパス
    • Year and Date
      2012-03-27
    • Related Report
      2012 Final Research Report
  • [Presentation] 独立分布でない場合の大数の法則の収束測度-ゲーム論的確率論からのアプローチ-2012

    • Author(s)
      宮部賢志・竹村彰通
    • Organizer
      2012日本数学会
    • Place of Presentation
      東京理科大学神楽坂キャンパス
    • Year and Date
      2012-03-27
    • Related Report
      2011 Annual Research Report
  • [Presentation] Bayesian logisticbetting strategy against probabilityforecasting2012

    • Author(s)
      Akimichi Takemura
    • Organizer
      The Fourth Workshop onGame-Theoretic Probability and RelatedTopics
    • Place of Presentation
      東京大学
    • Related Report
      2012 Final Research Report
  • [Presentation] Bayesian logistic betting strategy against probability forecasting2012

    • Author(s)
      Akimichi Takemura
    • Organizer
      The Fourth Workshop on Game-Theoretic Probability and Related Topics,
    • Place of Presentation
      東京大学
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Martingales andsequential tests from the viewpoint ofgame-theoretic probability2011

    • Author(s)
      Akimichi Takemura
    • Organizer
      Stanford seminar
    • Place of Presentation
      StanfordUniversity、California、 USA
    • Year and Date
      2011-08-04
    • Related Report
      2012 Final Research Report
  • [Presentation] Martingales and sequential tests from the viewpoint of game-theoretic probability2011

    • Author(s)
      Akimichi Takemura
    • Organizer
      Stanford stat seminar
    • Place of Presentation
      Stanford University California, USA(招待講演)
    • Year and Date
      2011-08-04
    • Related Report
      2011 Annual Research Report
  • [Presentation] Sequential optimizing strategy inmulti-dimensional bunded forecastinggames2010

    • Author(s)
      公文雅之、竹村 彰通、竹内 啓
    • Organizer
      日本数学会・2010 年度秋季総合分科会
    • Place of Presentation
      名古屋大学千種キャンパス
    • Related Report
      2012 Final Research Report
  • [Presentation] ゲーム論的確率論の最近の発展について2010

    • Author(s)
      竹村 彰通
    • Organizer
      科学研究費集会「計算代数手 法に基づく数理統計学の展開」
    • Place of Presentation
      大宮ソニックシティ-
    • Related Report
      2012 Final Research Report
  • [Presentation] Sequential optimizing strategy in multi-dimensional bunded forecasting games2010

    • Author(s)
      公文雅之, 竹村彰通, 竹内啓
    • Organizer
      日本数学会・2010年度秋季総合分科会
    • Place of Presentation
      名古屋大学千種キャンパス
    • Related Report
      2010 Annual Research Report
  • [Presentation] ゲーム論的確率論の最近の発展について2010

    • Author(s)
      竹村彰通
    • Organizer
      科学研究費集会「計算代数手法に基づく数理統計学の展開」
    • Place of Presentation
      大宮ソニックシティー
    • Related Report
      2010 Annual Research Report
  • [Remarks]

    • URL

      http://park.itc.u-tokyo.ac.jp/atstat/athp/projects_links.html

    • Related Report
      2012 Final Research Report
  • [Remarks] Research projects and links

    • URL

      http://park.itc.u-tokyo.ac.jp/atstat/athp/projects_links.html

    • Related Report
      2012 Annual Research Report
  • [Remarks]

    • URL

      http://park.itc.u-tokyo.ac.jp/atstat/athp/projects_links.html

    • Related Report
      2011 Annual Research Report

URL: 

Published: 2010-08-23   Modified: 2019-07-29  

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