Enlargement of filtration generated by semimartingales and its applications to mathematical finance

• Project/Area Number: 18540133
• 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: University of the Ryukyus
• Principal Investigator: YAMAZATO Makoto University of the Ryukyus, 理学部, 教授 (00015900)
• Co-Investigator(Kenkyū-buntansha): アルトゥロ コハツーヒガ (コハツ-ヒガ アルトゥーロ / KOHATSU-HIGA Artuto / コハツーヒガ アルトゥロ) 大阪大学, 大学院・基礎工学研究科, 准教授 (80420412)
• Project Period (FY): 2006 – 2008
• Project Status: Completed (Fiscal Year 2008)
• Budget Amount: ¥3,900,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥600,000); Fiscal Year 2008: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2007: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2006: ¥1,300,000 (Direct Cost: ¥1,300,000)
• Keywords: セミマルチンゲール / フィルターの拡大 / コンペンセーター / インサイダー / 対数効用

Research Abstract

セミマルチンゲールのフィルトレーションの種々の拡大のもとでのセミマルチンゲール分解を求めた. それをもとにレヴィ過程のフィルトレーションの種々の拡大における compensator を、utility の計算がしやすいような具体的な形で求めた. さらにレヴィ過程において満期の株価に関する情報が満期前では不鮮明な場合の、満期におけるlogarithmicutility が有限になるための必要十分条件を与えた。

Research Products

• [Journal Article] On a J_1-convergence theorem for stochastic processes on D[0, ∞) having monotone sample paths and its applications (2009)
  • Author(s): M. Yamazato
  • Journal Title: RIMS kokyuroku 1620 Pages: 109-118
• [Journal Article] On a J_1 convergence theorem for stochastic processes on D(0, ∞)having monotone sample paths and its applications. (2009)
  • Author(s): Makoto Yamazato
  • Journal Title: RIMS kokyuroku 1620 Pages: 109-118
• [Journal Article] Enlargement of filtrations with random times for processes with jumps (2008)
  • Author(s): A. Kohatsu-Higa, M. Yamazato
  • Journal Title: Stochastic Proc. Appl 118 Pages: 1136-1158
  • Peer Reviewed
• [Journal Article] Enlargement of filtrations with random times for processes with jumps. (2008)
  • Author(s): A. Kohatsu-Higa, M. Yamazato.
  • Journal Title: Stochastic Proc. Appl. 118 Pages: 1136-1158
  • Peer Reviewed
• [Journal Article] Enlargement of filtrations with random times for processes with jumps (2008)
  • Author(s): A. Kohatsu-Higa. and M. Yamazato
  • Journal Title: To appear in Stochastic Processes and their applications (in press)
  • Peer Reviewed
• [Journal Article] An Optimal Control Variance Reduction Method for Density Estimation (2008)
  • Author(s): A. Kebaier and A. Kohatsu-Higa
  • Journal Title: To appear in Stochastic Processes and their applications. (in press)
  • Peer Reviewed
• [Journal Article] A convolution approach to multivariate Bessel processes (2007)
  • Author(s): T. V. Nguyen, S. Ogawa, M. Yamazato
  • Journal Title: Stochastic processes and applications to mathematical finance 4 Pages: 233-244
  • Peer Reviewed
• [Journal Article] Insider problems for markets driven by L\'evy processes (2007)
  • Author(s): A. Kohatsu-Higa, M. Yamazato
  • Journal Title: Harmonic, wavelet and p-adic analysis 2 Pages: 363-381
  • Peer Reviewed
• [Journal Article] Models for insider trading with finite utility. (2007)
  • Author(s): A. Kohatsu-Higa
  • Journal Title: Lecture Notes in Mathematics 1919 Pages: 103-172
  • Peer Reviewed
• [Journal Article] Insider problems for markets driven by Levy processes (2007)
  • Author(s): A.Kohatsu-Higa, M.Yamazato
  • Journal Title: Abstract and Applied Analysis 2(To appear)
• [Journal Article] de Finetti's theorem for o-finite measures on R∞＼{0} (2007)
  • Author(s): K.Yamauchi, M.yamazato
  • Journal Title: Ryukyu Mathematical Journal 19 Pages: 129-136
• [Journal Article] de Finetti's theorem for σ-finite measures on R ∞ (2006)
  • Author(s): K. Yamauchi, M. Yamazato
  • Journal Title: Ryukyu Math. J 19 Pages: 129-136
• [Journal Article] Topics related to gamma processes (2006)
  • Author(s): M. Yamazato
  • Journal Title: Stochastic processes and applications to mathematical finance 3 Pages: 157-182
  • Peer Reviewed
• [Journal Article] A duality approach for the weak approximations of stochastic differential equations (2006)
  • Author(s): E.Clement, A.Kohatsu-Higa, D, Lamberton
  • Journal Title: Annals of Applied Probability 16 Pages: 1124-1154
• [Presentation] On a J_1 convergence theorem for stochastic processes on D [0, ∞) having monotone sample paths and its applications (2008)
  • Author(s): Makoto Yamazato
  • Organizer: The 8-th Workshop on stochastic Numerics
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 2008-07-08
• [Presentation] On a J1-convergence theorem for stochastic processes on D[0, ∞) having monotone sample paths and its applications (2008)
  • Organizer: The 8-th Workshop on Stochastic Numerics
  • Place of Presentation: Kyoto University
  • Year and Date: 2008-06-08
• [Presentation] First passage times for storage processes A survey, Workshop on Mathematical Finance and Stochastic (2006)
  • Organizer: Control, Osaka university
  • Place of Presentation: Holiday inKyoto