Theory of infinitely divisible distributions and its application

• Project/Area Number: 20540110
• 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: Hitotsubashi University
• Principal Investigator: FUJITA Takahiko Hitotsubashi University, 大学院・商学研究科, 教授 (50144316)
• Project Period (FY): 2008 – 2010
• Project Status: Completed (Fiscal Year 2010)
• Budget Amount: ¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000); Fiscal Year 2010: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2009: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2008: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
• Keywords: コーシー分布 / 逆正弦分布 / 指数分布 / ウィグナー分布 / リーマンゼータ関数 / バーゼル問題 / フルビッツゼータ関数 / オイラー公式 / 伊藤公式 / 保険数理 / ブラウン運動 / ランダムウォーク / Stock Option / Black Scholes Model / 無限分解可能分布 / Gamma Convolution / 確率論 / 一様列 / 確率分布 / p進整数

Research Abstract

Special values of the Riemann zeta function are evaluated by various probabilistic methods. These results were reported at the various domestic and international symposium. We investigated pricing of catastrophe options and discrete HJB eqution. Exotic stock options are investigated. Also Van der Corut sequence in padic integers are researched.

Research Products

• [Journal Article] Discrionete stochastic calculus and its application to discrete HJB equation (2011)
  • Author(s): 藤田岳彦, 石村直之
  • Journal Title: Advances in Mathematical Economics
  • Peer Reviewed
• [Journal Article] Special values of the Riemann zeta function via arcsine variables, Infinitely divisible processes and Related topics 15 (2011)
  • Author(s): 藤田岳彦
  • Journal Title: The Institute of Statistical Mathematics Cooperative Research Report 262 Pages: 70-79
• [Journal Article] Special values of the Hurwitz zeta function via generalized Cauchy variables, Infinitely divisible processes and Related topics 15 (2011)
  • Author(s): Fujita Takahiko, Yano Yuko
  • Journal Title: The Institute of Statistical Mathematics Cooperative Research Report 262 Pages: 62-69
• [Journal Article] Special values of the Riemann zeta function via arcsine variables (2011)
  • Author(s): Fujita Takahiko
  • Journal Title: Institute of Statistical Mathematics Cooperative Research Report Volume: 262 Pages: 70-79
• [Journal Article] Special values of the Hurwitz zeta function via generalized Cauchy variables (2011)
  • Author(s): Fujita Takahiko, Yano Yuko
  • Journal Title: Institute of Statistical Mathematics Cooperative Research Report Volume: 262 Pages: 62-69
• [Journal Article] Discrionete stochastic calculus and its application to discrete HJB equation (2011)
  • Author(s): Fujita Takahiko, Ishimura Naoyuki
  • Journal Title: Advances in Mathematical Economics Volume: 印刷中
• [Journal Article] A discrete analogue of two "dual" continuous GGC(:Generalized Gamma Convolution variables), Infinitely divisible processes and Related topics 14 (2010)
  • Author(s): 藤田岳彦
  • Journal Title: The Institute of Statistical Mathematics Cooperative Research Report 247 Pages: 87-91
• [Journal Article] Valuation of a Repriceable Executive Stock Option (2010)
  • Author(s): Fujita Takahiko, Ishii Masahiro
  • Journal Title: Asia-Pacific Financial Markets Vol.17, No.1 Pages: 1-18
  • Peer Reviewed
• [Journal Article] Valuation of a Repriceable Executive Stock Option (2010)
  • Author(s): Fujita Takahiko, Ishii Masahiro
  • Journal Title: Asia-Pacific Financial Markets Vol. 17 Pages: 1-18
  • Peer Reviewed
• [Journal Article] A discrete analogue of two "dual" continuous GGC(Generalized Gamma Convolution variables) (2010)
  • Author(s): 藤田岳彦
  • Journal Title: The Institute of Statistical Mathematics Cooperative Research Report 247巻 Pages: 87-91
• [Journal Article] 離散伊藤公式とその応用(数値解析における理論・手法・応用) (2009)
  • Author(s): 藤田岳彦、石村直之
  • Journal Title: 京都大学数理解析研究所講究録 1638 Pages: 130-136
• [Journal Article] 離散伊藤公式とその応用(数値解析における理論・手法・応用) (2009)
  • Author(s): 藤田岳彦, 石村直之
  • Journal Title: 京都大学数理解析研究所講究録 1638 Pages: 130-136
• [Journal Article] Matsumoto Shin, A uniformly distributed sequence on the ring of p.adic integers (2008)
  • Author(s): Fujita Takhiko, Kaneko Hiroshi
  • Journal Title: Monte Carlo Methods and Applications Vol.14 No.4 Pages: 303-310
  • Peer Reviewed
• [Journal Article] Tanaka Daichi, An arbitrage approach to the pricing of catasrophe options involving the Cox process (with Ishumura, N. and Tanaka, D.) (2008)
  • Author(s): 藤田岳彦, 石村直之
  • Journal Title: Hitotsubashi J.of Economics Vol 49 Pages: 67-74
  • Peer Reviewed
• [Journal Article] A probabilstic approach to the special values of the Riemann zeta function (2008)
  • Author(s): 藤田岳彦
  • Journal Title: 京都大学数理解析研究所講究録 1590 Pages: 1-9
• [Journal Article] Euler's formulae for the Riemann zeta function and Cauchy variables, Infinitely divisible processes and Related topics 12 (2008)
  • Author(s): 藤田岳彦
  • Journal Title: The Institute of Statistical Mathematics Cooperative Research Report 213 Pages: 98-103
• [Journal Article] Euler's formulae for the Riemann zeta function and Cauchy variables Infinitely divisible processes and Related topics 12 (2008)
  • Author(s): Fujita, Takahiko
  • Journal Title: The Institute of Statistical Mathematics Cooperative Research Report 213 Pages: 98-103
• [Journal Article] A probabilistic approach to special values of the Riemann zeta function (2008)
  • Author(s): 藤田岳彦
  • Journal Title: 京都大学数理解析研究所講究録 1590 Pages: 1-9
• [Journal Article] A UNIFORMLY DISTRIBUTED SEQUENCE ON THE RING OF p-ADIC INTEGERS. (2008)
  • Author(s): Fujita, Takahiko (with Kaneko, Matsumoto)
  • Journal Title: Monte Carlo Methods and Applications 14 Pages: 303-310
  • Peer Reviewed
• [Journal Article] An arbitrage approach to the pricing of catasrophe options involving the Cox process (共著) (2008)
  • Author(s): Fujita, Takahiko (with Ishimura, Tanaka)
  • Journal Title: Hitotsubashi J. of Economics Vol 49, 76-74 2008大学・研究所等紀要 49 Pages: 67-74
  • Peer Reviewed
• [Presentation] Special values of the Riemann zeta function via arcsine random variables (2011)
  • Author(s): Fujita Takahiko
  • Organizer: Analysis Seminar
  • Place of Presentation: Hitotsubashi Univ, Tokyo
  • Year and Date: 2011-01-29
• [Presentation] Special values of the Riemann zeta function via aresine random variables (2011)
  • Author(s): Fujita Takahiko
  • Organizer: Analysis seminaz
  • Place of Presentation: Hitotsubashi Univ.(招待講演)
  • Year and Date: 2011-01-29
• [Presentation] Special values of the Riemann zeta function via probability theory (2010)
  • Author(s): Fujita Takahiko
  • Organizer: School on Randomness and Information
  • Place of Presentation: Pucon, Chillie.
  • Year and Date: 2010-12-14
• [Presentation] Special values of the Riemann zeta function via probability theory (2010)
  • Author(s): Fujita Takahiko
  • Organizer: School on Randomness and Information
  • Place of Presentation: Pucon, Chillie
  • Year and Date: 2010-12-14
• [Presentation] Special values of the Riemann zeta function via arcsine random variables (2010)
  • Author(s): Fujita Takahiko
  • Organizer: Infinitely divisible distributions and its applications
  • Place of Presentation: The Institute of Statistical Mathematics, Tokyo.
  • Year and Date: 2010-11-05
• [Presentation] Special values of the Riemann zeta function via arcsine random variables (2010)
  • Author(s): Fujita Takahiko
  • Organizer: Infinitely divisible distributions and its applications
  • Place of Presentation: The Institute of Statistical Mathematics (Tokyo)
  • Year and Date: 2010-11-05
• [Presentation] Special values of the Riemann zeta function via arcsine random variables (2010)
  • Author(s): Fujita Takahiko
  • Organizer: Number Theory and Probability
  • Place of Presentation: Kyoto Univ, Kyoto.
  • Year and Date: 2010-09-13
• [Presentation] Special values of the Riemann zeta function via arcsine random variables (2010)
  • Author(s): Fujita Takahiko
  • Organizer: Number theory and Probability
  • Place of Presentation: Kyoto Univ.Research Institute for Mathematical Sciences(招待講演)
  • Year and Date: 2010-09-13
• [Presentation] On Some functional of Browninan Motion and Random Walk (2010)
  • Author(s): Fujita Takahiko
  • Organizer: Moscow University Probability Seminar
  • Place of Presentation: Moscow University, Moscow.
  • Year and Date: 2010-03-22
• [Presentation] On some functional ob Brownian Motion and Random Walk (2010)
  • Author(s): Fujita Takahiko
  • Organizer: Moscow University Probability seminar
  • Place of Presentation: Moscow, Moscow University
  • Year and Date: 2010-03-22
• [Presentation] On Restrat Options (2009)
  • Author(s): Fujita Takahiko
  • Organizer: Japan Russia Probability and Mathematical Statistics Symposium
  • Place of Presentation: Steklov Institute, Moscow.
  • Year and Date: 2009-09-15
• [Presentation] Pricing Restart Options (2009)
  • Author(s): Fujita Takahiko
  • Organizer: Japan Russia Probability and Mathematical Statistics Sympojium
  • Place of Presentation: Moscow, Steklov Institute
  • Year and Date: 2009-09-15
• [Presentation] On Restrat Options (2009)
  • Author(s): Fujita Takahiko
  • Organizer: International Financial Engneering Education Symposium
  • Place of Presentation: Hitotsubashi University, Tokyo.
  • Year and Date: 2009-08-08
• [Presentation] On Restart Options (2009)
  • Author(s): Fujita Takahiko
  • Organizer: International Financial Engeneering education Sympojium
  • Place of Presentation: Tokyo, Hitotsubashi University
  • Year and Date: 2009-08-08
• [Presentation] Pricing Restrat Options (2009)
  • Author(s): Fujita Takahiko
  • Organizer: Stochastic Analysis and Financial Engneering International Symposium
  • Place of Presentation: Kyoto Research Park, Kyoto.
  • Year and Date: 2009-08-05
• [Presentation] On Restart Options (2009)
  • Author(s): Fujita Takahiko
  • Organizer: Stochastic Analysis and Financial Engeneering International symposium
  • Place of Presentation: Kyoto, Kyoto Research Park
  • Year and Date: 2009-08-05
• [Presentation] An arbitrage approach to pricing options with insurance apprications (2009)
  • Author(s): Kawai Norihisa
  • Organizer: Fujita Takahiko, Ishimura Naoyuki, Africomp 2009
  • Place of Presentation: Suncity, South Africa.
  • Year and Date: 2009-01-07
• [Presentation] An arbitrage approach to pricing options with insuranceapplications (2009)
  • Author(s): Kawai, Norihisa(with Fujita, T, Ishimura, N)
  • Organizer: Africomp 2009
  • Place of Presentation: Suncity, South Africa
  • Year and Date: 2009-01-07
• [Presentation] A probalistic approach to the special values of the Riemann zeta function (2008)
  • Author(s): Fujita Takahiko
  • Organizer: School on Randomness and Information
  • Place of Presentation: Univ.of Santiago, Chillie
  • Year and Date: 2008-12-16
• [Presentation] A probabilistic approach to the special values of the Riemann zeta function (2008)
  • Author(s): Fujita, Takahiko
  • Organizer: School on Stochastics and Randomness
  • Place of Presentation: Univ. of Santiago, Chillie
  • Year and Date: 2008-12-16
• [Presentation] On some stochastic volatility model (2008)
  • Author(s): Fujita Takahiko
  • Organizer: 大阪大学金融保険中ノ島ワークショップ
  • Place of Presentation: 大阪
  • Year and Date: 2008-12-07
• [Presentation] On some stochastic volatility model (2008)
  • Author(s): Fujita, Takahiko
  • Organizer: 大阪大学金融保険中之島ワークショップ
  • Place of Presentation: 大阪大学 中之島
  • Year and Date: 2008-12-07
• [Book] 弱点克服 大学生の確率統計 (2010)
  • Author(s): 藤田岳彦
  • Total Pages: 260
  • Publisher: 東京図書
• [Book] ランダムウォークと確率解析 -ギャンブルから数理ファイナンスまで- (2008)
  • Author(s): 藤田岳彦
  • Total Pages: 291
  • Publisher: 日本評論社
• [Book] ファイナンス保険数理の現代的課題 (2008)
  • Author(s): 黒田耕嗣(藤田岳彦 共著)
  • Total Pages: 232
  • Publisher: 日本大学文理学部