Applications of the Wiener functionals

• Project/Area Number: 24540143
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Chuo University
• Principal Investigator: FUJITA Takahiko 中央大学, 理工学部, 教授 (50144316)
• Project Period (FY): 2012-04-01 – 2016-03-31
• Project Status: Completed (Fiscal Year 2015)
• Budget Amount: ¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000); Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2014: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2012: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
• Keywords: ブラウン運動 / 確率微分方程式 / ブラック・ショールズ・モデル / リーマンゼータ関数 / ウィーナー汎関数 / リスク評価 / 金融工学 / 保険数理 / 伝染モデル / ポアソン過程 / ブラック・ショールズモデル / エキゾティックオプション / デリバティブ / ランダム・ウォーク / レヴィ過程モデル / 確率解析 / 離散確率解析 / ゼータ関数 / 確率論 / 数論

Outline of Final Research Achievements

Through　this research period, we investigate applications of Wiener functinals to
number theory (especially the Riemann Zeta functions), to financial engineering (new exotic options), to fusion of financial engineering and actuarial mathematics. We publish many research papers about applications of the Wiener functionals.

Research Products

• [Journal Article] Estimate on the Risk of Epidemic Outbreaks for an Insurer: A Simple Stochastic Model (2015)
  • Author(s): Chiaki Ishii, Naoyuki Ishimura, takahiko Fujita
  • Journal Title: International Journal of Modeling and Optimization Volume: 5 Issue: 2 Pages: 161-165
  • DOI: 10.7763/ijmo.2015.v5.454
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Journal Article] ルックバックオプションの価格付けとヘッジ (2015)
  • Author(s): 藤田岳彦 川西泰裕
  • Journal Title: 数理解析研究所講究録 ファイナンスの数理解析とその応用 Volume: 1933 Pages: 13-21
• [Journal Article] ブラック・ショールズモデルとCGMYモデルの下でのルックバックオプションの価格付け (2015)
  • Author(s): 藤田岳彦 川西泰裕
  • Journal Title: 統計数理研究所共同研究リポート Volume: 350 Pages: 44-58
• [Journal Article] A generalization of Carry process (2014)
  • Author(s): Fujita, T. Nakano, F. Sadahiro, T.
  • Journal Title: Discerete Mathematics and Theoretical Computer Science Volume: 1 Pages: 61-70
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] On the one-sided maximum of Brownian and random walk fragments and its applications to new exotic options called "meander option " (2014)
  • Author(s): Fujita, T., Kawanishi, Y. , Yor, M.
  • Journal Title: Pacific Journal of Mathematical Industry Volume: 6.2 Pages: 1-7
  • NAID: 40020377829
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Journal Article] A model of the instantaneous interest rate in discrete processes (2013)
  • Author(s): Naoyuki Ishimura, Takahiko Fujita, and Masaaki Nakamura
  • Journal Title: Procedia Economics and Finance Volume: 5 Pages: 355-360
  • DOI: 10.1016/s2212-5671(13)00042-7
  • Peer Reviewed
• [Journal Article] Discerte stochastic calculus and its applications (2012)
  • Author(s): T. Fujita, N. Ishimura, N. Kawai
  • Journal Title: Advances in Mathematical Ecomics Volume: 16 Pages: 119-131
  • Peer Reviewed
• [Journal Article] Special values of the Hurwitz zeta function via generalized Cauchy variables (2012)
  • Author(s): T. Fujita , Y. Yano
  • Journal Title: Kyoto Journal of Mathematics Volume: Vol. 52, No. 3. Pages: 465-478
  • Peer Reviewed
• [Presentation] On some Extensions of the Parisian Option (2015)
  • Author(s): Yasuhiro KAWANISHI, Taklahiko FUJITA
  • Organizer: RIMS Work shop on Financial Modeling and Analysis
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 2015-11-16
• [Presentation] Estimate on the RIsk of Epidemic Outbreaks for an Insurer:A Simple Stochastic MOdel (2015)
  • Author(s): Chiaki Ishii、Naoyuki Ishimura, Takahiko Fujita
  • Organizer: 2015 7th INternational COnference on COmputer Research and Development
  • Place of Presentation: Ho CHi MInh City, Vietnam
  • Year and Date: 2015-02-06 – 2015-02-07
• [Presentation] CGMYモデルとブラック・ショールズモデルの下でのルックバックパワーオプションの価格付け (2014)
  • Author(s): 藤田岳彦 川西泰裕
  • Organizer: 無限分解可能分布論とその応用
  • Place of Presentation: 統計数理研究所
  • Year and Date: 2014-11-28 – 2014-11-29
• [Presentation] ルックバックパワーオプションの価格付けとヘッジ (2014)
  • Author(s): 藤田岳彦 川西泰裕
  • Organizer: ファイナンスの数理解析とその応用
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 2014-11-25 – 2014-11-27
• [Presentation] Pricing of lookback power options (2014)
  • Author(s): Fujita, T., Kawanishi, Y>
  • Organizer: The 46th International Symposium on Stochastic System Thery and Its Applications
  • Place of Presentation: Kyoto INstitute of Technology
  • Year and Date: 2014-11-01 – 2014-11-02
• [Presentation] A generalization of carry process (2014)
  • Author(s): FUJITA, T. NAKANO、 F., SADAHIRO, T.
  • Organizer: International symposium on Formal Power SEries and Algebraic COmbinatorics
  • Place of Presentation: Chicago, USA
  • Year and Date: 2014-06-30 – 2014-07-02
• [Presentation] Ｒｉｅｍａｎｎ ｚｅｔａ ｆｕｎｃｔｉｏｎ ａｎｄ Ｐｒｏｂａｂｉｌｉｔｙ ｔｈｅｏｒｙ (2014)
  • Author(s): Ｔａｋａｈｉｋｏ ＦＵＪＩＴＡ
  • Organizer: ｓｔｏｃｈａｓｔｉｃ ａｎａｌｙｓｉｓ ｓｙｍｐｏｓｉｕｍ ｉｎ ＲＩＭＳ
  • Place of Presentation: ＲＩＭＳ Ｋｙｏｔｏ Ｕｎｉｖｅｒｓｉｔｙ
  • Invited
• [Book] 解いて学ぶがロア理論 (2013)
  • Author(s): 藤田武彦
  • Total Pages: 256
  • Publisher: 東京図書