Stochastic calculus for Levy processes

• Project/Area Number: 18540183
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Ehime 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: ¥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。

Research Products

• [Journal Article] Composition with distributions of Wiener-Poisson variables and its asymptotic expansion (2009)
  • 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
  • Peer Reviewed
• [Journal Article] Malliavin calculus applied to mathematical finance and a new formulation of the integration-by-parts (2009)
  • Author(s): Ishikawa, Yasushi
  • Journal Title: 数理解析研究所講究録 1620 Pages: 67-80
• [Journal Article] Composition with distributions of Wiener-Poisson variables and its asymptotic expansion (2009)
  • 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
  • Peer Reviewed
• [Journal Article] Malliavin calculus applied to mathematical finance and a new formulation of the integration-by-parts (2009)
  • Author(s): Ishikawa Yasushi
  • Journal Title: 数理解析研究所講究録 1620 Pages: 67-80
• [Journal Article] Optimal consumption models in economic growth (2008)
  • Author(s): Morimoto, Hiroaki
  • Journal Title: J. Math. Anal. Appl. 337 Pages: 480-492
  • 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
  • Peer Reviewed
• [Journal Article] Optimal stopping problem associated with jump-diffusion processes (2008)
  • Author(s): Yasushi ISHIKAWA
  • Journal Title: preprint
• [Journal Article] Optimal Consumption Control Problem associated with Jump-Diffusion Processes (2008)
  • Author(s): Yasushi Ishikawa Hiroaki Morimoto
  • Journal Title: preprint
• [Journal Article] Optimal consumption models in economic growth (2008)
  • Author(s): Morimoto Hiroaki
  • Journal Title: J. Math. Anal. Appl 337 Pages: 480-492
  • Peer Reviewed
• [Journal Article] Optimal consumption models in economic growth (2008)
  • Author(s): Morimoto Hiroaki
  • Journal Title: J.Math.Anal.Appl 337 Pages: 480-492
  • 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)
  • Peer Reviewed
• [Journal Article] Optimal control problem associated with jump-diffusion processes and optimal stopping (2007)
  • Author(s): Ishikawa, Yasushi
  • Journal Title: 数理解析研究所講究録 1529 Pages: 42-63
• [Journal Article] Optimal control problem associated with jump-diffusion processes and optimal stopping (2007)
  • Author(s): Ishikawa Yasushi
  • Journal Title: 数理解析研究所講究録 1529 Pages: 42-63
  • Peer Reviewed
• [Journal Article] Optimal Control Problem Associated with Jump Processes (2007)
  • Author(s): Ishikawa, Yasushi
  • Journal Title: 数理解析研究所講究録 (To appear)
• [Journal Article] Malliavin calculus applied to mathematical finance and a new formulation of the integration-by-parts (2006)
  • Author(s): Ishikawa, Yasushi and Kunita, Hiroshi
  • Journal Title: Stochastic Processes and their Applications 116 Pages: 1743-1769
  • Peer Reviewed
• [Journal Article] The probabilistic solution of the Dirichlet problem for degenerate elliptic equations (2006)
  • Author(s): Morimoto, Hiroaki
  • Journal Title: Bulletin of the Polish Academy of Sciences 54 Pages: 163-174
  • Peer Reviewed
• [Journal Article] Malliavin calculus applied to mathematical finance and a new formulation of the integration-by-parts (2006)
  • Author(s): Ishikawa, Yasushi
  • Journal Title: Stochastic Processes and their Applications 116・12 Pages: 1743-1769
• [Journal Article] The probabilistic solution of the Dirichlet problem for degenerate elliptic equations (2006)
  • Author(s): Morimoto, Hiroaki
  • Journal Title: Bulletin of the Polish Academy of Sciences 54・2 Pages: 163-174
• [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
• [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
• [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
• [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
• [Presentation] Optimal Consumption Control Problem associated with Jump-Diffusion Processes (2008)
  • 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
• [Presentation] Viscosity solutions of paraboric Hamilton-Jacobi equation in economic growth (2008)
  • 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
• [Presentation] Optimal Consumption Control Problem associated with Jump-Diffusion Processes (2008)
  • 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
• [Presentation] Optimal Consumption Control Problem associated with Jump-Diffusion Processes (2008)
  • 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
• [Presentation] Composition with distributions of Poisson variables and its asymptotic expansion (2007)
  • Author(s): Ishikawa Yasushi
  • Organizer: Levy Processes : Theory and Applications
  • Place of Presentation: Copenhagen University(poster)
  • Year and Date: 2007-08-13
• [Presentation] Composition with disthbutions of Poisson variables and its asymptotic expansion (2007)
  • Author(s): Ishikawa Yasushi
  • Organizer: Levy Processes:Theory and Applications
  • Place of Presentation: Copenhagen University
  • Year and Date: 2007-08-13
• [Presentation] 変分不等式の粘性解とAmerican put options (2006)
  • 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
• [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
• [Book] 基礎数学II (2008)
  • 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