Research on new numerical methods for simulations of diffusion processes based on Kusuoka approximation and their application to finance

2008 Fiscal Year Self-evaluation Report

• Project/Area Number: 18540113
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Tokyo Institute of Technology
• Principal Investigator: NINOMIYA Syoiti Tokyo Institute of Technology, 大学院・イノベーションマネジメント研究科, 教授 (70313377)
• Project Period (FY): 2006 – 2009
• Keywords: 確率論 / 数理工学 / アルゴリズム

Research Abstract

(1)楠岡近似の原理に従って確率微分方程式で記述される拡散過程の高次弱近似を過当とする、頑健で汎用的な数値計算アルゴリズムを発見・構成する
(2)数理ファイナンスへの応用によりその有用性を検証
(3)そのアルゴリズムが広く社会に受け入れられるように計算機プログラムを開発する

Research Products

• [Journal Article] A Remark on the Asymptotic Expansion of density function of Wiener Functionals (2009)
  • Author(s): S. Kusuoka and H. Osajima
  • Journal Title: J. Fuct. Analysis 255 Pages: 2545-2562
  • Peer Reviewed
• [Journal Article] Weak approximation of stochastic differential equations and application to derivative pricing (2008)
  • Author(s): Syoiti Ninomiya and Nicolas Victoir
  • Journal Title: Applied Mathematical Finance Vol.15, No.2 Pages: 107-121
  • Peer Reviewed
• [Journal Article] A new higher-order weak approximation scheme of stochastic differential equations and the Runge-Kutta method
  • Author(s): Syoiti Ninomiya and Mariko Ninomiya
  • Journal Title: Finance and Stochastics (to appear)
  • URL: http://arxiv.org/abs/0709.2434
  • Peer Reviewed
• [Presentation] A higher-order weak approximation method of SDEs and the Runge-Kutta method (2009)
  • Author(s): Syoiti Ninomiya
  • Organizer: Conference on small time asymptotics, perturbation theory and heat kernel methods in mathematical finance
  • Place of Presentation: Wolfgang Pauli Institute, Vienna
  • Year and Date: 20090210-12
• [Presentation] 確率微分方程式の新しい弱近似法 : 楠岡近似とそれを実現するアルゴリズム (2009)
  • Author(s): 二宮祥一
  • Organizer: 計算による数理科学の展開2009(研究集会)於神戸大学理学部
  • Place of Presentation: 神戸
  • Year and Date: 20090108-09
• [Presentation] Kusuoka Scheme : A new weak approximation methods of diffusion processes (2008)
  • Author(s): 二宮祥一
  • Organizer: 大阪大学金融保険教育研究センター主催中之島ワークショップ「金融工学・数理計量ファイナンスの諸問題2008」於大阪大学中之島センター
  • Place of Presentation: 大阪
  • Year and Date: 20081206-07
• [Presentation] Malliavin calculus and Computational Fimamce (2008)
  • Author(s): S. Kusuoka
  • Organizer: Seoul-Tokyo Conference
  • Place of Presentation: KIAS
  • Year and Date: 2008-11-21
• [Presentation] Malliavin calculus, Computational Fimamce (2008)
  • Author(s): S. Kusuoka
  • Organizer: Symposium in Honor of Kiyosi Ito : Stochastic Analysis and Its Impact in Mathematics and Science
  • Place of Presentation: Institute of Mathematical Sciences National Univ. Singapore
  • Year and Date: 2008-07-10
• [Presentation] Malliavin calculus, Computational Fimamce (2008)
  • Author(s): S. Kusuoka
  • Organizer: Minisymposium on stochastic analysis in the occasion of the award the Degree of a Doctor Honoris Causa to Professor Paul Malliavin
  • Place of Presentation: the Faculty of Mathematics and Natural Sciences of the University of Bonn
  • Year and Date: 2008-04-19
• [Presentation] 楠岡近似のアルゴリズムについて (2008)
  • Author(s): 二宮祥一
  • Organizer: ファイナンスのための数理ワークショップ於早稲田大学理工学部
  • Place of Presentation: 東京
  • Year and Date: 2008-04-04