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Numerical analysis for SDE and non-colliding stochastic processes

Research Project

Project/Area Number 17H06833
Research Category

Grant-in-Aid for Research Activity Start-up

Allocation TypeSingle-year Grants
Research Field Basic analysis
Research InstitutionOsaka University

Principal Investigator

Taguchi Dai  大阪大学, 基礎工学研究科, 助教 (70804657)

Research Collaborator Li Libo  
Ngo Hoang-Long  
Naganuma Nobuaki  
Tanaka Akihiro  
Project Period (FY) 2017-08-25 – 2019-03-31
Project Status Completed (Fiscal Year 2018)
Budget Amount *help
¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000)
Fiscal Year 2018: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2017: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Keywords確率微分方程式 / CIR過程 / Levy過程 / Euler-Maruyama近似 / Levy process / 非衝突確率過程 / Jump型CIR過程 / Dyson Brownian motion / Malliavin calculus / 数値解析
Outline of Final Research Achievements

Recently, CIR processes (Cox-Ingersoll-Ross processes) and CEV processes (constant elasticity of variance processes) are widely used in mathematical finance, and are extended in various directions, such as extending to the Jump type by using the Levy processes. These stochastic processes have some boundary conditions, such as not taking negative values or not staying at the boundary. The research achievements of this study are to introduce a discrete approximation scheme with the same boundary conditions as these stochastic processes, and provide their rate of convergence.

Academic Significance and Societal Importance of the Research Achievements

確率微分方程式に対する離散近似はEuler-Maruyama近似が広く用いられるが、対応する確率微分方程式と同様の境界条件を満たすとは限らない。本研究で得られた成果では、対応する確率微分方程式と同様の境界条件を持つ離散近似を構成することができ、近年広く研究されている境界付き確率過程に対する数値解析が可能となる。また、確率微分方程式は楕円型偏微分方程式と深い関係が知られているため、確率論を用いた数値解析(モンテカルロ法)を適用することができる。

Report

(3 results)
  • 2018 Annual Research Report   Final Research Report ( PDF )
  • 2017 Annual Research Report
  • Research Products

    (20 results)

All 2019 2018 2017 Other

All Int'l Joint Research (4 results) Journal Article (3 results) (of which Int'l Joint Research: 3 results,  Peer Reviewed: 3 results) Presentation (12 results) (of which Int'l Joint Research: 7 results,  Invited: 8 results) Remarks (1 results)

  • [Int'l Joint Research] University of New South Wales(オーストラリア)

    • Related Report
      2018 Annual Research Report
  • [Int'l Joint Research] Hanoi National University of Education(ベトナム)

    • Related Report
      2018 Annual Research Report
  • [Int'l Joint Research] Hanoi National University of Education(ベトナム)

    • Related Report
      2017 Annual Research Report
  • [Int'l Joint Research] University of New South Wales(オーストラリア)

    • Related Report
      2017 Annual Research Report
  • [Journal Article] On the Euler-Maruyama scheme for spectrally one-sided L\'evy driven SDEs with H\"older continuous coefficients2019

    • Author(s)
      Libo Li and Dai Taguchi
    • Journal Title

      Statistics & Probability Letters

      Volume: 146 Pages: 15-26

    • DOI

      10.1016/j.spl.2018.10.017

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] On a positivity preserving numerical scheme for jump-extended CIR process: the alpha-stable case2019

    • Author(s)
      Libo Li and Dai Taguchi
    • Journal Title

      BIT Numerical Mathematics

      Volume: 印刷中

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Approximation for non-smooth functionals of stochastic differential equations with irregular drift2018

    • Author(s)
      Hoang-Long Ngo and Dai Taguchi
    • Journal Title

      Journal of Mathematical Analysis and Applications

      Volume: 457 Issue: 1 Pages: 361-388

    • DOI

      10.1016/j.jmaa.2017.08.006

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Presentation] On the Euler-Maruyama scheme for degenerate SDEs with non-sticky boundary condition2019

    • Author(s)
      Dai Taguchi
    • Organizer
      Stochastic processes and related topics
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Implicit Euler-Maruyama scheme for non-colliding particle systems2018

    • Author(s)
      Dai Taguchi
    • Organizer
      Workshop on "Mathematical finance and related issues"
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Semi-implicit Euler-Maruyama scheme for non-colliding particle systems2018

    • Author(s)
      Dai Taguchi
    • Organizer
      13th International Conference in Monte Carlo & Quasi-Monte Carlo Methods in Scientific Computing
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Semi-implicit Euler-Maruyama scheme for non-colliding particle systems2018

    • Author(s)
      Dai Taguchi
    • Organizer
      The 12th AIMS Conference on Dynamical Systems, Differential Equations and Applications
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research
  • [Presentation] On a positivity preserving scheme for the alpha-CIR process2018

    • Author(s)
      Dai Taguchi
    • Organizer
      Ritsumeikan Workshop on Probability Theory and its Applications to Insurance and Finance
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Jump型CIR過程の離散近似について2018

    • Author(s)
      Dai Taguchi
    • Organizer
      金融工学・数理計量ファイナンスの諸問題 2018
    • Related Report
      2018 Annual Research Report
    • Invited
  • [Presentation] Implicit Euler-Maruyama scheme for non-colliding particle systems2018

    • Author(s)
      Dai Taguchi
    • Organizer
      Workshop on Mathematical finance and related issues
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Semi-implicit Euler-Maruyama scheme for non-colliding particle systems2017

    • Author(s)
      Dai Taguchi
    • Organizer
      九州確率論セミナー
    • Related Report
      2017 Annual Research Report
    • Invited
  • [Presentation] 確率微分方程式の解の一意性について2017

    • Author(s)
      Dai Taguchi
    • Organizer
      確率論ヤングサマーセミナー
    • Related Report
      2017 Annual Research Report
    • Invited
  • [Presentation] Discrete approximations for non-colliding SDEs2017

    • Author(s)
      Dai Taguchi
    • Organizer
      確率解析シンポジウム
    • Related Report
      2017 Annual Research Report
  • [Presentation] Discrete approximations for non-colliding SDEs2017

    • Author(s)
      Dai Taguchi
    • Organizer
      確率論シンポジウム(ショートコミュニケーション)
    • Related Report
      2017 Annual Research Report
  • [Presentation] On the Euler-Maruyama scheme for SDEs with discontinuous diffusion coefficient2017

    • Author(s)
      Dai Taguchi
    • Organizer
      International Conference on Monte Carlo Methods and Applications
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Remarks] Research page of Dai Taguchi

    • URL

      https://sites.google.com/view/daitaguchi/home

    • Related Report
      2017 Annual Research Report

URL: 

Published: 2017-08-25   Modified: 2020-03-30  

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