• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to previous page

Stochastic calculus for Levy processes

Research Project

Project/Area Number 18540183
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Basic analysis
Research InstitutionEhime University

Principal Investigator

ISHIKAWA Yasushi  Ehime University, 大学院・理工学研究科, 准教授 (70202976)

Co-Investigator(Kenkyū-buntansha) MORIMOTO Hiroaki  愛媛大学, 大学院・理工学研究科, 教授 (80166438)
Project Period (FY) 2006 – 2008
Project Status Completed (Fiscal Year 2008)
Budget Amount *help
¥3,340,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥540,000)
Fiscal Year 2008: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2007: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2006: ¥1,000,000 (Direct Cost: ¥1,000,000)
Keywordsレビー過程 / 確率過程 / 漸近展開 / 確率微分方程式 / 確率解析
Research Abstract

加法過程のひとつであるレビー過程について、Malliavin解析、漸近展開、確率的コントロール問題の3つの側面から研究をおこなった。このうち、漸近展開、確率的コントロール問題に関しては、数理ファイナンスと密接に関連する成果を得た。成果は研究会で発表された。また、論文にまとめられ、すでに出版されたか、または印刷中、投稿中である。

Report

(4 results)
  • 2008 Annual Research Report   Final Research Report ( PDF )
  • 2007 Annual Research Report
  • 2006 Annual Research Report
  • Research Products

    (31 results)

All 2009 2008 2007 2006

All Journal Article (18 results) (of which Peer Reviewed: 10 results) Presentation (11 results) Book (2 results)

  • [Journal Article] Composition with distributions of Wiener-Poisson variables and its asymptotic expansion2009

    • Author(s)
      Ishikawa, Yasushi
    • Journal Title

      統計数理研究所共同研究リポート 225

      Pages: 82-91

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Malliavin calculus applied to mathematical finance and a new formulation of the integration-by-parts2009

    • Author(s)
      Ishikawa, Yasushi
    • Journal Title

      数理解析研究所講究録 1620

      Pages: 67-80

    • Related Report
      2008 Final Research Report
  • [Journal Article] Composition with distributions of Wiener-Poisson variables and its asymptotic expansion2009

    • Author(s)
      Ishikawa Yasushi
    • Journal Title

      統計数理研究所共同研究リポート 225

      Pages: 82-91

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Malliavin calculus applied to mathematical finance and a new formulation of the integration-by-parts2009

    • Author(s)
      Ishikawa Yasushi
    • Journal Title

      数理解析研究所講究録 1620

      Pages: 67-80

    • Related Report
      2008 Annual Research Report
  • [Journal Article] Optimal consumption models in economic growth2008

    • Author(s)
      Morimoto, Hiroaki
    • Journal Title

      J. Math. Anal. Appl. 337

      Pages: 480-492

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] レビー過程に関連した確率変数の連続性と絶対連続性2008

    • Author(s)
      Ishikawa, Yasushi and Thomas, Simon
    • Journal Title

      統計数理研究所共同研究リポート 213

      Pages: 104-132

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Optimal stopping problem associated with jump-diffusion processes2008

    • Author(s)
      Yasushi ISHIKAWA
    • Journal Title

      preprint

    • Related Report
      2008 Final Research Report
  • [Journal Article] Optimal Consumption Control Problem associated with Jump-Diffusion Processes2008

    • Author(s)
      Yasushi Ishikawa Hiroaki Morimoto
    • Journal Title

      preprint

    • Related Report
      2008 Final Research Report
  • [Journal Article] Optimal consumption models in economic growth2008

    • Author(s)
      Morimoto Hiroaki
    • Journal Title

      J. Math. Anal. Appl 337

      Pages: 480-492

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Optimal consumption models in economic growth2008

    • Author(s)
      Morimoto Hiroaki
    • Journal Title

      J.Math.Anal.Appl 337

      Pages: 480-492

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] レビー過程に関連した確率変数の連続性と絶対連続性2008

    • Author(s)
      Y. Ishikawa and T. Simon
    • Journal Title

      統計数理研究所共同研究リポート 213(印刷中)

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Optimal control problem associated with jump-diffusion processes and optimal stopping2007

    • Author(s)
      Ishikawa, Yasushi
    • Journal Title

      数理解析研究所講究録 1529

      Pages: 42-63

    • Related Report
      2008 Final Research Report
  • [Journal Article] Optimal control problem associated with jump-diffusion processes and optimal stopping2007

    • Author(s)
      Ishikawa Yasushi
    • Journal Title

      数理解析研究所講究録 1529

      Pages: 42-63

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Optimal Control Problem Associated with Jump Processes2007

    • Author(s)
      Ishikawa, Yasushi
    • Journal Title

      数理解析研究所講究録 (To appear)

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Malliavin calculus applied to mathematical finance and a new formulation of the integration-by-parts2006

    • Author(s)
      Ishikawa, Yasushi and Kunita, Hiroshi
    • Journal Title

      Stochastic Processes and their Applications 116

      Pages: 1743-1769

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] The probabilistic solution of the Dirichlet problem for degenerate elliptic equations2006

    • Author(s)
      Morimoto, Hiroaki
    • Journal Title

      Bulletin of the Polish Academy of Sciences 54

      Pages: 163-174

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Malliavin calculus applied to mathematical finance and a new formulation of the integration-by-parts2006

    • Author(s)
      Ishikawa, Yasushi
    • Journal Title

      Stochastic Processes and their Applications 116・12

      Pages: 1743-1769

    • Related Report
      2006 Annual Research Report
  • [Journal Article] The probabilistic solution of the Dirichlet problem for degenerate elliptic equations2006

    • Author(s)
      Morimoto, Hiroaki
    • Journal Title

      Bulletin of the Polish Academy of Sciences 54・2

      Pages: 163-174

    • Related Report
      2006 Annual Research Report
  • [Presentation] Composition with distributions of Wiener-Poisson variables and its asymptotic expansion(II)2009

    • Author(s)
      石川保志
    • Organizer
      Stochastic Analysis and Statistical Inference IV
    • Place of Presentation
      東京大学
    • Year and Date
      2009-02-18
    • Related Report
      2008 Final Research Report
  • [Presentation] Composition with distributions of Wiener-Poisson variables and its asymptotic expansion (II)2009

    • Author(s)
      石川 保志
    • Organizer
      Stochastic Analysis and Statistical Inference IV
    • Place of Presentation
      東京大学
    • Year and Date
      2009-02-18
    • Related Report
      2008 Annual Research Report
  • [Presentation] Composition with distributions of Wiener-Poisson variables and its asymptotic expansion(I)2008

    • Author(s)
      石川保志
    • Organizer
      Stochastic Analysis and Statistical Inference III
    • Place of Presentation
      東京大学
    • Year and Date
      2008-11-26
    • Related Report
      2008 Final Research Report
  • [Presentation] Composition with distributions of Wiener-Poisson variables and its asymptotic expansion (I)2008

    • Author(s)
      石川 保志
    • Organizer
      Stochastic Analysis and Statistical Inference III
    • Place of Presentation
      東京大学
    • Year and Date
      2008-11-26
    • Related Report
      2008 Annual Research Report
  • [Presentation] Optimal Consumption Control Problem associated with Jump-Diffusion Processes2008

    • Author(s)
      石川保志
    • Organizer
      無限分解可能過程に関連する諸問題
    • Place of Presentation
      統計数理研究所
    • Year and Date
      2008-11-08
    • Related Report
      2008 Annual Research Report 2008 Final Research Report
  • [Presentation] Viscosity solutions of paraboric Hamilton-Jacobi equation in economic growth2008

    • Author(s)
      森本宏明
    • Organizer
      広島応用解析セミナー
    • Place of Presentation
      広島大学
    • Year and Date
      2008-09-02
    • Related Report
      2008 Annual Research Report 2008 Final Research Report
  • [Presentation] Optimal Consumption Control Problem associated with Jump-Diffusion Processes2008

    • Author(s)
      石川保志
    • Organizer
      The 8th workshop on "Stochastic Numerics"
    • Place of Presentation
      京都大学
    • Year and Date
      2008-07-08
    • Related Report
      2008 Final Research Report
  • [Presentation] Optimal Consumption Control Problem associated with Jump-Diffusion Processes2008

    • Author(s)
      石川 保志
    • Organizer
      The 8^<th> workshop on “Stochastic Numerics"
    • Place of Presentation
      京都大学
    • Year and Date
      2008-07-08
    • Related Report
      2008 Annual Research Report
  • [Presentation] Composition with distributions of Poisson variables and its asymptotic expansion2007

    • Author(s)
      Ishikawa Yasushi
    • Organizer
      Levy Processes : Theory and Applications
    • Place of Presentation
      Copenhagen University(poster)
    • Year and Date
      2007-08-13
    • Related Report
      2008 Final Research Report
  • [Presentation] Composition with disthbutions of Poisson variables and its asymptotic expansion2007

    • Author(s)
      Ishikawa Yasushi
    • Organizer
      Levy Processes:Theory and Applications
    • Place of Presentation
      Copenhagen University
    • Year and Date
      2007-08-13
    • Related Report
      2007 Annual Research Report
  • [Presentation] 変分不等式の粘性解とAmerican put options2006

    • Author(s)
      森本宏明
    • Organizer
      微分方程式の漸近問題と粘性解理論
    • Place of Presentation
      富山大学
    • Related Report
      2008 Final Research Report
  • [Book] 理工系数学入門2008

    • Author(s)
      柳 重則・大塚 寛・石川 保志, ほか
    • Total Pages
      116
    • Publisher
      愛媛大学基礎数学編集委員会
    • Related Report
      2007 Annual Research Report
  • [Book] 基礎数学II2008

    • Author(s)
      柳 重則・大塚 寛・石川 保志
    • Total Pages
      85
    • Publisher
      愛媛大学基礎数学編集委員会
    • Related Report
      2007 Annual Research Report

URL: 

Published: 2006-04-01   Modified: 2016-04-21  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi