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Applications of the Wiener functionals

Research Project

Project/Area Number 24540143
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionChuo University

Principal Investigator

FUJITA Takahiko  中央大学, 理工学部, 教授 (50144316)

Project Period (FY) 2012-04-01 – 2016-03-31
Project Status Completed (Fiscal Year 2015)
Budget Amount *help
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2014: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2012: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Keywordsブラウン運動 / 確率微分方程式 / ブラック・ショールズ・モデル / リーマンゼータ関数 / ウィーナー汎関数 / リスク評価 / 金融工学 / 保険数理 / 伝染モデル / ポアソン過程 / ブラック・ショールズモデル / エキゾティックオプション / デリバティブ / ランダム・ウォーク / レヴィ過程モデル / 確率解析 / 離散確率解析 / ゼータ関数 / 確率論 / 数論
Outline of Final Research Achievements

Through this research period, we investigate applications of Wiener functinals to
number theory (especially the Riemann Zeta functions), to financial engineering (new exotic options), to fusion of financial engineering and actuarial mathematics. We publish many research papers about applications of the Wiener functionals.

Report

(5 results)
  • 2015 Annual Research Report   Final Research Report ( PDF )
  • 2014 Research-status Report
  • 2013 Research-status Report
  • 2012 Research-status Report
  • Research Products

    (16 results)

All 2015 2014 2013 2012

All Journal Article (8 results) (of which Peer Reviewed: 6 results,  Open Access: 2 results,  Acknowledgement Compliant: 3 results) Presentation (7 results) (of which Invited: 1 results) Book (1 results)

  • [Journal Article] Estimate on the Risk of Epidemic Outbreaks for an Insurer: A Simple Stochastic Model2015

    • Author(s)
      Chiaki Ishii, Naoyuki Ishimura, takahiko Fujita
    • Journal Title

      International Journal of Modeling and Optimization

      Volume: 5 Issue: 2 Pages: 161-165

    • DOI

      10.7763/ijmo.2015.v5.454

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] ルックバックオプションの価格付けとヘッジ2015

    • Author(s)
      藤田岳彦 川西泰裕
    • Journal Title

      数理解析研究所講究録 ファイナンスの数理解析とその応用

      Volume: 1933 Pages: 13-21

    • Related Report
      2014 Research-status Report
  • [Journal Article] ブラック・ショールズモデルとCGMYモデルの下でのルックバックオプションの価格付け2015

    • Author(s)
      藤田岳彦 川西泰裕
    • Journal Title

      統計数理研究所共同研究リポート

      Volume: 350 Pages: 44-58

    • Related Report
      2014 Research-status Report
  • [Journal Article] A generalization of Carry process2014

    • Author(s)
      Fujita, T. Nakano, F. Sadahiro, T.
    • Journal Title

      Discerete Mathematics and Theoretical Computer Science

      Volume: 1 Pages: 61-70

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] On the one-sided maximum of Brownian and random walk fragments and its applications to new exotic options called "meander option "2014

    • Author(s)
      Fujita, T., Kawanishi, Y. , Yor, M.
    • Journal Title

      Pacific Journal of Mathematical Industry

      Volume: 6.2 Pages: 1-7

    • NAID

      40020377829

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] A model of the instantaneous interest rate in discrete processes2013

    • Author(s)
      Naoyuki Ishimura, Takahiko Fujita, and Masaaki Nakamura
    • Journal Title

      Procedia Economics and Finance

      Volume: 5 Pages: 355-360

    • DOI

      10.1016/s2212-5671(13)00042-7

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Discerte stochastic calculus and its applications2012

    • Author(s)
      T. Fujita, N. Ishimura, N. Kawai
    • Journal Title

      Advances in Mathematical Ecomics

      Volume: 16 Pages: 119-131

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Special values of the Hurwitz zeta function via generalized Cauchy variables2012

    • Author(s)
      T. Fujita , Y. Yano
    • Journal Title

      Kyoto Journal of Mathematics

      Volume: Vol. 52, No. 3. Pages: 465-478

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Presentation] On some Extensions of the Parisian Option2015

    • Author(s)
      Yasuhiro KAWANISHI, Taklahiko FUJITA
    • Organizer
      RIMS Work shop on Financial Modeling and Analysis
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2015-11-16
    • Related Report
      2015 Annual Research Report
  • [Presentation] Estimate on the RIsk of Epidemic Outbreaks for an Insurer:A Simple Stochastic MOdel2015

    • Author(s)
      Chiaki Ishii、Naoyuki Ishimura, Takahiko Fujita
    • Organizer
      2015 7th INternational COnference on COmputer Research and Development
    • Place of Presentation
      Ho CHi MInh City, Vietnam
    • Year and Date
      2015-02-06 – 2015-02-07
    • Related Report
      2014 Research-status Report
  • [Presentation] CGMYモデルとブラック・ショールズモデルの下でのルックバックパワーオプションの価格付け2014

    • Author(s)
      藤田岳彦 川西泰裕
    • Organizer
      無限分解可能分布論とその応用
    • Place of Presentation
      統計数理研究所
    • Year and Date
      2014-11-28 – 2014-11-29
    • Related Report
      2014 Research-status Report
  • [Presentation] ルックバックパワーオプションの価格付けとヘッジ2014

    • Author(s)
      藤田岳彦 川西泰裕
    • Organizer
      ファイナンスの数理解析とその応用
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2014-11-25 – 2014-11-27
    • Related Report
      2014 Research-status Report
  • [Presentation] Pricing of lookback power options2014

    • Author(s)
      Fujita, T., Kawanishi, Y>
    • Organizer
      The 46th International Symposium on Stochastic System Thery and Its Applications
    • Place of Presentation
      Kyoto INstitute of Technology
    • Year and Date
      2014-11-01 – 2014-11-02
    • Related Report
      2014 Research-status Report
  • [Presentation] A generalization of carry process2014

    • Author(s)
      FUJITA, T. NAKANO、 F., SADAHIRO, T.
    • Organizer
      International symposium on Formal Power SEries and Algebraic COmbinatorics
    • Place of Presentation
      Chicago, USA
    • Year and Date
      2014-06-30 – 2014-07-02
    • Related Report
      2014 Research-status Report
  • [Presentation] Riemann zeta function and Probability theory2014

    • Author(s)
      Takahiko FUJITA
    • Organizer
      stochastic analysis symposium in RIMS
    • Place of Presentation
      RIMS Kyoto University
    • Related Report
      2013 Research-status Report
    • Invited
  • [Book] 解いて学ぶがロア理論2013

    • Author(s)
      藤田武彦
    • Total Pages
      256
    • Publisher
      東京図書
    • Related Report
      2012 Research-status Report

URL: 

Published: 2013-05-31   Modified: 2019-07-29  

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