Fluctuation theory of Levy processes and applications in risk management

• Project/Area Number: 22710143
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: Social systems engineering/Safety system
• Research Institution: Osaka University
• Principal Investigator: YAMAZAKI Kazutoshi 大阪大学, 金融・保険教育研究センター, 助教 (50554937)
• Project Period (FY): 2010 – 2012
• Project Status: Completed (Fiscal Year 2012)
• Budget Amount: ¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000); Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2011: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2010: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
• Keywords: 確率論 / リスクマネジメント / レヴィー過程 / 確率制御 / 最適停止

Research Abstract

We developed risk management models using Levy processes. In parallel to the work on the fluctuation theory of spectrally negative Levy processes, we worked on several risk management problems arising in finance and credit risk; we modeled them in terms of optimal stopping problems/games and obtained their solutions analytically and numerically.

Research Products

• [Journal Article] Default swap games driven by spectrally negative Levy processes (2013)
  • Author(s): M. Egami, T. Leung, K. Yamazaki
  • Journal Title: Stochastic Processes and their Applications Volume: 123(2) Pages: 347-384
  • Peer Reviewed
• [Journal Article] American step-up and step-down default swaps under Levy models (2013)
  • Author(s): T. Leung, K. Yamazaki
  • Journal Title: Quantitative Finance Volume: 13(1) Pages: 137-157
  • Peer Reviewed
• [Journal Article] Precautionay Measures for Credit Risk Management in Jump Models (2013)
  • Author(s): E. Egami, K. Yamazaki
  • Journal Title: Stochastics Volume: 85(1) Pages: 111-143
  • Peer Reviewed
• [Journal Article] Precautionary Measures for Credit Risk Management in Jump Models (2012)
  • Author(s): M.Egami, K.Yamazaki
  • Journal Title: Stochastics Volume: (掲載決定) Issue: 1 Pages: 111-143
  • DOI: 10.1080/17442508.2011.653566
  • Peer Reviewed
• [Journal Article] Asymptotically optimal Bayesian sequential change detection and identification rules (2012)
  • Author(s): Savas Dayanik, Warren Powell, Kazutoshi Yamazaki
  • Journal Title: Annals of Operations Research Volume: (掲載確定) Issue: 1 Pages: 337-370
  • DOI: 10.1007/s10479-012-1121-6
  • Peer Reviewed
• [Journal Article] Model-Free Implied Volatility: From Surface to Index (2011)
  • Author(s): M. Fukasawa, I. Ishida, N. Maghrebi, K. Oya, M. Ubukata, K. Yamazaki
  • Journal Title: International Journal of Theoretical and Applied Finance Volume: 14(4) Pages: 433-463
  • Peer Reviewed
• [Journal Article] 「解除可能クレジット・デフォルト・スワップの価格評価」 (2011)
  • Author(s): T. Leung, K. Yamazaki
  • 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」 Pages: 18-26
• [Journal Article] Asymptotically Optimal Bayesian Sequential Change Detection and Identification Rules
  • Author(s): S. Dayanik, W.B. Powell, K. Yamazaki
  • Journal Title: Annals of Operations Research
  • Peer Reviewed
• [Presentation] Optimal Dividends in the Dual Model (2013)
  • Author(s): K. Yamazaki
  • Organizer: International Workshop on Quantitative Finance
  • Place of Presentation: KAIST, Daejeon, Korea
  • Year and Date: 2013-03-18
• [Presentation] Optimal Dividends in the Dual Model for Spectrally Positive Levy Processes (2013)
  • Author(s): 山崎和俊
  • Organizer: マルコフ過程と確率解析
  • Place of Presentation: 京都大学
• [Presentation] Optimal Dividends in the Dual Model (2013)
  • Author(s): K. Yamazaki
  • Organizer: 国立清華大学
  • Place of Presentation: Hsinch, Taiwan
  • Invited
• [Presentation] Optimal Dividends in the Dual Model (2013)
  • Author(s): K. Yamazaki
  • Organizer: International Workshop on Quantitative Finance
  • Place of Presentation: KAIST, Korea
  • Invited
• [Presentation] Optimal Stopping Problems for Spectrally Negative Levy Processes and Applications in Finance (2012)
  • Author(s): K. Yamazaki
  • Organizer: Financial/Actuarial Mathematics Seminar
  • Place of Presentation: University of Michigan, Ann Arbor, USA
  • Year and Date: 2012-10-11
• [Presentation] Toward a Generalization of the Leland-Toft Model (2012)
  • Author(s): K. Yamazaki
  • Organizer: NUS-RMI Seminar
  • Place of Presentation: National University of Singapore, Singapore
  • Year and Date: 2012-04-05
• [Presentation] Toward a Generalization of the Leland-Toft model (2012)
  • Author(s): 山崎和俊
  • Organizer: Winter Workshop on Finance 2012
  • Place of Presentation: 北海道大学(北海道)(招待講演)
  • Year and Date: 2012-02-14
• [Presentation] Toward a Generalization of the Leland-Toft Model (2012)
  • Author(s): K. Yamazaki
  • Organizer: NUS-RMI Seminar
  • Place of Presentation: National University of Singapore
  • Invited
• [Presentation] Default Swap Games (2012)
  • Author(s): K. Yamazaki
  • Organizer: INFORMS International
  • Place of Presentation: Beijing, China
• [Presentation] Default Swap Games (2012)
  • Author(s): K. Yamazaki
  • Organizer: SIAM Conference on Financial Mathematics and Engineering
  • Place of Presentation: Minneapolis
• [Presentation] レヴィー過程の基礎とその応用 (2012)
  • Author(s): 山崎和俊
  • Organizer: 立命館大学
  • Place of Presentation: 滋賀
  • Invited
• [Presentation] Default Swap Games (2012)
  • Author(s): 山崎和俊
  • Organizer: Workshop on “Mathematical Finance and Related Issues”
  • Place of Presentation: 京都
• [Presentation] Optimal Stopping Problems for Spectrally Negative Levy Processes and Applications in Finance (2012)
  • Author(s): K. Yamazaki
  • Organizer: University of Michigan
  • Place of Presentation: Ann Arbor
  • Invited
• [Presentation] Default Swap Games (2012)
  • Author(s): K. Yamazaki
  • Organizer: INFORMS 2012
  • Place of Presentation: Phoenix
• [Presentation] Optimal Stopping Problems for Spectrally Negative Levy Processes and Applications in Finance (2012)
  • Author(s): K. Yamazaki
  • Organizer: University of California
  • Place of Presentation: Santa Barbara
  • Invited
• [Presentation] Contraction options and optimal multiple-stopping in spectrally negative Levy models (2012)
  • Author(s): 山崎和俊
  • Organizer: 近経研究会
  • Place of Presentation: 横浜国立大学
  • Invited
• [Presentation] Optimal Stopping Problems for Spectrally Negative Levy Processes (2012)
  • Author(s): 山崎和俊
  • Organizer: 関西確率論セミ ナー
  • Place of Presentation: 京都大学
  • Invited
• [Presentation] Phase-type Fitting Approximation of Overshoot/Undershoot Distributions for Spectrally Negative Levy Processes (2011)
  • Author(s): K. Yamazaki
  • Organizer: 確率論シンポジウム
  • Place of Presentation: 関西大学
  • Year and Date: 2011-12-19
• [Presentation] Phase-tyrpe Fitting Approximation of Overshoot/Undershoot Distributions for Spectrally Negative Levy Processes (2011)
  • Author(s): 山崎和俊
  • Organizer: 確率論シンポジウム
  • Place of Presentation: 関西大学(大阪府)
  • Year and Date: 2011-12-19
• [Presentation] Toward a Generalization of the Leland-Toft model (2011)
  • Author(s): 山崎和俊
  • Organizer: 横浜国立大学・南山大学共同ファイナンス・ワークショップ
  • Place of Presentation: 横浜国立大学(神奈川県)(招待講演)
  • Year and Date: 2011-12-04
• [Presentation] Optimal Stopping Problems for Spectrally Negative Levy Processes and Applications in Finance (2011)
  • Author(s): 山崎和俊
  • Organizer: JAFEEファイナンスの意思決定解析研究部会
  • Place of Presentation: 芝浦工業大学(東京都)(招待講演)
  • Year and Date: 2011-11-26
• [Presentation] Toward a Generalization of the Leland-Toft Model (2011)
  • Author(s): 山崎和俊
  • Organizer: 第一回数理ファイナンス合宿型セミナー
  • Place of Presentation: リフレフォーラム(東京都)
  • Year and Date: 2011-11-05
• [Presentation] Optimal Stopping Problems for Spectrally Negative Levy Processes and Applications inFinance (2011)
  • Author(s): K. Yamazaki
  • Organizer: The 43rd ISCIE International Symposium on Stochastic Systems Theory and Its Applications
  • Place of Presentation: 立命館大学
  • Year and Date: 2011-10-29
• [Presentation] Optimal Stopping Problems for Spectrally Negative Levy Processes and Applications in Finance (2011)
  • Author(s): 山崎和俊
  • Organizer: The 43^<rd> ISCIE International Symposium on Stochastic Systems Theory and its Applications
  • Place of Presentation: 立命館大学(滋賀県)
  • Year and Date: 2011-10-29
• [Presentation] Default Swap Games (2011)
  • Author(s): 山崎和俊
  • Organizer: JAFEE夏季大会
  • Place of Presentation: 慶応大学(東京都)
  • Year and Date: 2011-10-15
• [Presentation] Default Swap Games (2011)
  • Author(s): K. Yamazaki
  • Organizer: JAFEE 夏季大会
  • Place of Presentation: 慶応大学
  • Year and Date: 2011-10-14
• [Presentation] Default Swap Games (2011)
  • Author(s): 山崎和俊
  • Organizer: First international conference on financial engineering and Risk Management application
  • Place of Presentation: Bandung (Indonesia)(招待講演)
  • Year and Date: 2011-09-26
• [Presentation] Default Swap Games (2011)
  • Author(s): K. Yamazaki
  • Organizer: 日本オペレーションズ・リサーチ学会秋季研究発表会
  • Place of Presentation: 甲南大学
  • Year and Date: 2011-09-16
• [Presentation] Default Swap Games (2011)
  • Author(s): 山崎和俊
  • Organizer: 日本オペレーションズ・リサーチ学会
  • Place of Presentation: 甲南大学(兵庫県)
  • Year and Date: 2011-09-16
• [Presentation] Pricing American Step-up and Step-down Credit Default Swaps under Levy Models (2011)
  • Author(s): K. Yamazaki
  • Organizer: Young Researchers Workshop on Finance 2011
  • Place of Presentation: 首都大学東京
  • Year and Date: 2011-03-04
• [Presentation] American Step-Up and Step-Down Credit Default Swaps under Levy Models (2011)
  • Author(s): 山崎和俊、Tim Siu-tang Leung
  • Organizer: Young Researcher's Workshop on Finance 2011
  • Place of Presentation: 東京
  • Year and Date: 2011-03-04
• [Presentation] American Step-Up and Step-Down Credit Default Swaps under Levy Models (2011)
  • Author(s): 山崎和俊、Tim Siu-tang Leung
  • Organizer: Modeling and Managing Financial Risks
  • Place of Presentation: フランス・パリ
  • Year and Date: 2011-01-12
• [Presentation] On Scale Functions of Spectrally Negative Levy Processes with Phase-type Jumps (2010)
  • Author(s): 山崎和俊、江上雅彦
  • Organizer: Quantitative Methods in Finance
  • Place of Presentation: オーストラリア・シドニー
  • Year and Date: 2010-12-16
• [Presentation] Model-free Implied Volatility: From Surface to Index (2010)
  • Author(s): K. Yamazaki
  • Organizer: 大阪大学中之島ワークショップ
  • Place of Presentation: 中之島センター, 大阪
  • Year and Date: 2010-12-03
• [Presentation] American Step-UP and Step-Down Credit Default Swaps under Levy Models (2010)
  • Author(s): 山崎和俊、Tim Siu-tang Leung
  • Organizer: Financial Modeling and Analysis
  • Place of Presentation: 京都
  • Year and Date: 2010-11-24
• [Presentation] On Scale Functions of Spectrally Negative Levy Processes with Phase-type Jumps (2010)
  • Author(s): 山崎和俊、江上雅彦
  • Organizer: Workshop on "Mathematical Finance and Related Issues"
  • Place of Presentation: 京都
  • Year and Date: 2010-09-13
• [Presentation] On Scale Functions of Spectrally Negative Levy Processes with Phase-type Jumps (2010)
  • Author(s): K. Yamazaki
  • Organizer: Workshop on "Mathematical Finance and Related Issues,"
  • Place of Presentation: 京都リサーチパーク, 京都
  • Year and Date: 2010-09-12
• [Presentation] On Scale Functions of Spectrally Negative Levy Processes with Phase-type Jumps (2010)
  • Author(s): K. Yamazaki
  • Organizer: The 34th Conference on Stochastic Processes and Their Applications
  • Place of Presentation: 千里ライフサイエンスセンター,大阪
  • Year and Date: 2010-09-09
• [Presentation] On Scale Functions of Spectrally Negative Levy Processes with Phase-type Jumps (2010)
  • Author(s): 山崎和俊、江上雅彦
  • Organizer: The 34^<th> Conference on Stochastic Processes and Their Applications
  • Place of Presentation: 大阪
  • Year and Date: 2010-09-09
• [Presentation] On Scale Functions of Spectrally Negative Levy Processes with Phase-type Jumps (2010)
  • Author(s): K. Yamazaki
  • Organizer: KIER-TMUInternational Workshop on Financial Engineering 2010
  • Place of Presentation: 首都大学東京
  • Year and Date: 2010-08-02
• [Presentation] On Scale Functions of Spectrally Negative Levy Processes with Phase-type Jumps (2010)
  • Author(s): 山崎和俊、江上雅彦
  • Organizer: KIER-TMU International Workshop on Financial Engineering 2010
  • Place of Presentation: 東京
  • Year and Date: 2010-08-02
• [Presentation] Precautionary Measures for Credit Risk Management in Jump Models (2010)
  • Author(s): K. Yamazaki
  • Organizer: JAFEE 夏季大会
  • Place of Presentation: 成城大学
  • Year and Date: 2010-07-31
• [Presentation] Precautionary Measures for Credit Risk Management in Jump Models (2010)
  • Author(s): 山崎和俊、江上雅彦
  • Organizer: JAFEE大会2010年夏
  • Place of Presentation: 東京
  • Year and Date: 2010-07-31
• [Presentation] Asymptotic Theory of Detection and Identification of an Unobservable Change in the Distribution of a Markov-Modulated Random Sequence (2010)
  • Author(s): 山崎和俊、Savas Dayanik
  • Organizer: International Workshop in Applied Probability 2010
  • Place of Presentation: スペイン・マドリッド
  • Year and Date: 2010-07-07
• [Presentation] On Scale Functions of Spectrally Negative Levy Processes with Phase-type Jumps (2010)
  • Author(s): K. Yamazaki
  • Organizer: 阪大確率論セミナー
  • Place of Presentation: 大阪大学
  • Year and Date: 2010-06-29
• [Presentation] On Scale Functions of Spectrally Negative Levy Processes with Phase-type Jumps (2010)
  • Author(s): 山崎和俊、江上雅彦
  • Organizer: 阪大確率論セミナー
  • Place of Presentation: 大阪(招待講演)
  • Year and Date: 2010-06-29
• [Presentation] On Scale Functions of Spectrally Negative Levy Processes with Phase-type Jumps (2010)
  • Author(s): K. Yamazaki
  • Organizer: 九州確率論セミナー
  • Place of Presentation: 九州大学
  • Year and Date: 2010-06-04
• [Presentation] On Scale Functions of Spectrally Negative Levy Processes With Phase-type Jumps (2010)
  • Author(s): 山崎和俊、江上雅彦
  • Organizer: 九州確率論セミナー
  • Place of Presentation: 福岡(招待講演)
  • Year and Date: 2010-06-04
• [Presentation] Precautionary Measures for Credit Risk Management in Jump Models (2010)
  • Author(s): 山崎和俊、江上雅彦
  • Organizer: Workshop&Spring School on Stochastic Calculus and Applications
  • Place of Presentation: 台湾・台北
  • Year and Date: 2010-04-16
• [Remarks]
  • URL: https://sites.google.com/site/kyamazak/
• [Remarks] Kazutoshi Yamazaki
  • URL: https://sites.google.com/site/kyamazak/
• [Remarks]
  • URL: http://www-csfi.sigmath.es.osaka-u.ac.jp/faculty/personal/yamazaki/index.html
• [Remarks]
  • URL: http://www-csfi.sigmath.es.osaka-u.ac.jp/faculty/personal/yamazaki/index.html