Research on multi-period Value Measure and Finance-Actuary

2008 Fiscal Year Final Research Report

• Project/Area Number: 17340023
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: The University of Tokyo
• Principal Investigator: KUSUOKA Shigeo The University of Tokyo, 大学院・数理科学研究科, 教授 (00114463)
• Co-Investigator(Renkei-kenkyūsha): YOSHIDA Nakahiro 東京大学, 大学院・数理科学研究科, 教授 (90210707) ; TAKAHASHI Akihiko 東京大学, 大学院・経済学研究科, 教授 (50313226)
• Project Period (FY): 2005 – 2008
• Keywords: 確率論 / ファイナンス、リスクの計量化 / 数値数学

Research Abstract

(1) 離散時間多期間リスク尺度の時間間隔をゼロに近づけたときの極限の研究した、及び法則不変な凸リスク尺度の特徴付け定理の簡略な証明を与えた
(2) 同分布を持つ独立な確率変数の和に関する研究
(3) 拡散過程に関する期待値を高速に求める手法の研究

Research Products

• [Journal Article] Consistent estimation of covariation under nonsynchronicity, Stat (2008)
  • Author(s): Hayashi, T., S. Kusuoka
  • Journal Title: Inference Stoch. Process11 no.1 Pages: 93-106
• [Journal Article] 株式利益の希薄化を考慮した転換価格修正条項付き転換社債の価格について (2008)
  • Author(s): 楠岡成雄
  • Journal Title: 金融研究 第27巻第2号 Pages: 119-147
• [Journal Article] A Remark on the Asymptotic Expansion of density function of Wiener Functionals (2008)
  • Author(s): S. Kusuoka, H.Osajima
  • Journal Title: J. Fuct. Analysis 255 Pages: 2545-2562
• [Journal Article] Homogeneous Law Invariant Multiperiod Value Measures and their Limits (2007)
  • Author(s): S. Kusuoka, Y. Morimoto
  • Journal Title: J. Math. Sci. Univ. Tokyo 14 Pages: 117-156
• [Journal Article] A Remark on Law Invariant Convex Risk Measures, in Advances in Mathematical Economics ed. S.Kusuoka (2007)
  • Author(s): S. Kusuoka
  • Journal Title: M. Maruyama vol.10 Pages: 91-100
• [Presentation] Malliavin calculus and Computational Fimamce (2008)
  • Author(s): S. Kusuoka
  • Organizer: Seoul-Tokyo Conference, KIAS
  • Year and Date: 2008-11-21
• [Presentation] Malliavin calculus and Computational Fimamce, Symposium in Honor of Kiyosi Ito : Stochastic Analysis and Its Impact in Mathematics and Science, Institute of Mathematical Sciences (2008)
  • Author(s): S. Kusuoka
  • Organizer: National Univ.Singapore
  • Year and Date: 2008-07-10
• [Presentation] Malliavin calculus and Computational Fimamce, Minisymposium on stochastic analysis in the occasion of the award the Degree of a Doctor Honoris Causa to Professor Paul Malliavin (2008)
  • Author(s): S. Kusuoka
  • Organizer: the Faculty of Mathematics and Natural Sciences of the University of Bonn
  • Year and Date: 2008-04-19