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The Research on precise estimate for the regularity of diffusion Operator of diffusion process with absorbed boundary condition and Its application

Research Project

Project/Area Number 22540174
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Basic analysis
Research InstitutionThe University of Tokyo

Principal Investigator

KUSUOKA Shigeo  東京大学, 大学院・数理科学研究科, 教授 (00114463)

Project Period (FY) 2010 – 2012
Project Status Completed (Fiscal Year 2012)
Budget Amount *help
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2012: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2011: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2010: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Keywords確率解析 関数解析 / ファイナンス / 拡散過程 / マリアバン解析 / 数値計算 / 吸収壁 / 基本解の精密評価 / 確率的メッシュ法 / デリバティブ / 拡散作用素の精密評価 / ディリクレ境界条件
Research Abstract

We studied the property and numerical computation methods for solutions of diffusion equation related to diffusion processes with absorbed boundary (Dirichlet boundary) which appears in pricing knock-out derivatives. First, we studied about precise estimates of smoothness for diffusion operators with Dirichlet boundary condition, and obtained similar estimates to estimates in the case of diffusion operators without boundary conditions. Then we studied numerical computation methods for the expectation of diffusion process with an absorbed boundary. We studied a similar method to KLNV method in the case of no boundary conditions, and obtained 3rdorder approximation formula. Unfortunately Whitakker function appears in the formula,the implementation is difficult, and so we could not do the computer simulation.

Report

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

    (18 results)

All 2013 2012 2011 2010 Other

All Journal Article (11 results) (of which Peer Reviewed: 11 results) Presentation (7 results) (of which Invited: 1 results)

  • [Journal Article] Gaussian K-Scheme:Justification for KLNV method2013

    • Author(s)
      Kusuoka Shigeo S.Kusuoka, M.Maruyama
    • Journal Title

      Advances in Mathematical Economics

      Volume: vol,17(to appear)

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] A remark on credit risk models and copula2013

    • Author(s)
      KUSUOKA Shigeo
    • Journal Title

      Advances in Mathematical Economics

      Volume: 16 Pages: 53-84

    • NAID

      40021336957

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Classical mechanical model of Brownian motion with one particle coupled to a random wave field2013

    • Author(s)
      KUSUOKA Shigeo
    • Journal Title

      Stochastic Analysis and its Application

      Volume: 30 Pages: 493-528

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A Remark on Malliavin calculus: Uniform Estimate and Localization2012

    • Author(s)
      Kusuoka Shigeo
    • Journal Title

      J. Math. Sci. Univ. Tokyo

      Volume: 19 Pages: 533-558

    • NAID

      120005678224

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Classical mechanical model of Brownian motion with one particle coupled to a random wave field2012

    • Author(s)
      Kusuoka Shigeo, and Liang Song
    • Journal Title

      Stoch. Anal. Appl

      Volume: 30,no,3 Pages: 493-528

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] A remark on credit risk models and copula2012

    • Author(s)
      Kusuoka Shigeo, and Nakashima Takanobu
    • Journal Title

      Advances in Mathematical Economics ed. S.Kusuoka, M.Maruyama

      Volume: vol.16 Pages: 53-84

    • NAID

      40021336957

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] A remark on credit risk models and copula2012

    • Author(s)
      KUSUOKA, Shigeo
    • Journal Title

      Advances in Mathematical Economics

      Volume: 16

    • NAID

      40021336957

    • Related Report
      2011 Annual Research Report 2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A certain Limit of Iterated CTE2010

    • Author(s)
      Kusuoka Shigeo
    • Journal Title

      Advances in Mathematical Economics ed. S.Kusuoka, M.Maruyama

      Volume: vol,13 Pages: 99-111

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Uniform Estimate for distributions of the sum of i.i.d. random variables with fat tail2010

    • Author(s)
      Fushiya Hirotaka and Kusuoka Shigeo
    • Journal Title

      J. Math. Sci. Univ. Tokyo

      Volume: 17 Pages: 79-121

    • NAID

      120006906036

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Large Deviation for stochastic line integrals as Lp current Prob2010

    • Author(s)
      Kuwada Kazumasa, Kusuoka Shigeo andTamura Yozo
    • Journal Title

      Theory Related Fields

      Volume: 147 Pages: 649-674

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Acalassical mechanical model of Brownian motion with plural particles2010

    • Author(s)
      Kusuoka Shigeo and Liang Song
    • Journal Title

      Reviews in Math. Physics

      Volume: 22 Pages: 733-838

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Presentation] A remark on credit risk models and copula, CREST and 4th Ritsumeikan-Frorence Workshop on Risk, Simulation and related Topics2012

    • Organizer
      立命館大学 APU
    • Place of Presentation
      別府
    • Related Report
      2012 Final Research Report
  • [Presentation] Numerical Computation for the Expectation on Diffusion Processes2011

    • Author(s)
      KUSUOKA Shigeo
    • Organizer
      ICIAM 2011 (International Congres on Industrial and Applied Mathematics)
    • Place of Presentation
      バンクーバー,カナダ(招待講演)
    • Year and Date
      2011-07-21
    • Related Report
      2011 Annual Research Report
  • [Presentation] Numerical Computation for the Expectation on Diffusion Processes2011

    • Author(s)
      KUSUOKA, Shigeo
    • Organizer
      ICIAM 2011 (International Congres on Industrial and Applied Mathematics)
    • Place of Presentation
      バンクーバー、カナダ
    • Year and Date
      2011-07-21
    • Related Report
      2010 Annual Research Report
  • [Presentation] Numerical Computation for theExpectation on Diffusion Processes2011

    • Organizer
      ICIAM2011, Vancouver
    • Related Report
      2012 Final Research Report
  • [Presentation] Approximation of Expectation of Diffusion Processes, Analysis, Stochastics, Applications2010

    • Organizer
      ウィーン大学
    • Related Report
      2012 Final Research Report
  • [Presentation] Topics on Leading-edge2010

    • Organizer
      NumericalProcedures and Models
    • Place of Presentation
      東京工業大学
    • Related Report
      2012 Final Research Report
  • [Presentation] A remark on credit risk models and copula

    • Author(s)
      KUSUOKA, Shigeo
    • Organizer
      JAFEE-Columbia-ISM International Conference on Financial Mathematics, Engineering and Statistics
    • Place of Presentation
      統計数理研究所 立川キャンパス, 東京
    • Related Report
      2012 Annual Research Report
    • Invited

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

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