Resolvents of stochastic processes with jumps and applications in maturity randomization

• Project/Area Number: 26800092
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Foundations of mathematics/Applied mathematics
• Research Institution: Kansai University
• Principal Investigator: Yamazaki Kazutoshi 関西大学, システム理工学部, 准教授 (50554937)
• Project Period (FY): 2014-04-01 – 2017-03-31
• Project Status: Completed (Fiscal Year 2016)
• Budget Amount: ¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000); Fiscal Year 2016: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000); Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2014: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
• Keywords: レヴィー過程 / レゾルベント / 数理ファイナンス / 保険数学 / 在庫管理

Outline of Final Research Achievements

We analyzed the resolvents of the spectrally negative Levy process and other jump processes. As an application for maturity randomization, we approximated the solution to multiple stopping problems with refraction times using the resolvents and phase-type fitting. We also obtained the resolvents of the controlled process under the (s,S)-policy and the refracted-reflected processes via the scale function, and applied them to solve optimal dividend problems and inventory control problems.

Research Products

• [Journal Article] On the Refracted-Reflected Spectrally Negative Levy Processes (2017)
  • Author(s): J. L. Perez and K. Yamazaki
  • Journal Title: Stochastic Processes and their Applications Volume: 印刷中
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Phase-type Approximation of the Gerber-Shiu Function (2017)
  • Author(s): K. Yamazaki
  • Journal Title: the Journal of the Operations Research Society of Japan (special issue of the 60th anniversary of the Operations Research Society of Japan). Volume: 印刷中
  • NAID: 130005874224
  • Peer Reviewed
• [Journal Article] On the Joint Reflective and Refractive Dividend Strategies in Spectrally Positive Levy Models (2017)
  • Author(s): B. Avanzi, J. L. Perez, B. Wong, and K. Yamazaki
  • Journal Title: Insurance: Mathematics and Economics Volume: 72 Pages: 148-162
  • DOI: 10.1016/j.insmatheco.2016.10.010
  • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
• [Journal Article] Refraction-Reflection Strategies in the Dual Model (2017)
  • Author(s): J. L. Perez and K. Yamazaki
  • Journal Title: ASTIN Bulletin Volume: 47(1) Issue: 1 Pages: 199-238
  • DOI: 10.1017/asb.2016.28
  • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
• [Journal Article] Inventory Control for Spectrally Positive Levy Demand Processes (2016)
  • Author(s): K. Yamazaki
  • Journal Title: Mathematics of Operations Research Volume: 印刷中
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Optimality of Refraction Strategies for Spectrally Negative Levy Processes (2016)
  • Author(s): D. Hernandez-Hernandez, J. L. Perez, and K. Yamazaki
  • Journal Title: SIAM Journal on Control and Optimization Volume: 印刷中
  • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
• [Journal Article] Optimal Multiple Stopping with Negative Discount Rate and Random Refraction Times under Levy Models (2015)
  • Author(s): T. Leung, K. Yamazaki, and H. Zhang
  • Journal Title: SIAM Journal on Control and Optimization Volume: 53 Issue: 4 Pages: 2373-2405
  • DOI: 10.1137/140957317
  • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
• [Journal Article] An Analytic Recursive Method for Optimal Multiple Stopping: Canadization and Phase-Type Fitting (2015)
  • Author(s): T. Leung, K. Yamazaki and H. Zhang
  • Journal Title: International Journal of Theoretical and Applied Finance Volume: 印刷中
  • Peer Reviewed
• [Journal Article] Optimality of Doubly Reflected Levy Processes in Singular Control (2015)
  • Author(s): E. J. Baurdoux and K. Yamazaki
  • Journal Title: Stochastic Processes and their Applications Volume: 印刷中
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Optimal Double Stopping of a Brownian Bridge (2015)
  • Author(s): E. J. Baurdoux, N. Chen, B. A. Surya and K. Yamazaki
  • Journal Title: Advances in Applied Probability Volume: 印刷中
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Contraction Options and Optimal Multiple-Stopping in Spectrally Negative Levy Models (2015)
  • Author(s): K. Yamazaki
  • Journal Title: Applied Mathematics and Optimization Volume: 印刷中
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Games of Singular Control and Stopping Driven by Spectrally One-sided Levy Processes (2015)
  • Author(s): D. Hernandez-Hernandez and K. Yamazaki
  • Journal Title: Stochastic Processes and their Applications Volume: 印刷中
  • Peer Reviewed / Acknowledgement Compliant
• [Presentation] On optimal joint reflective and refractive dividend strategies in spectrally positive Levy models (2017)
  • Author(s): K. Yamazaki
  • Organizer: Osaka-UCL Workshop on Stochastics, Numerics and Risk
  • Place of Presentation: 大阪大学
  • Int'l Joint Research / Invited
• [Presentation] Optimality of Doubly Reflected Levy Processes in Singular Control (2016)
  • Author(s): K. Yamazaki
  • Organizer: Workshop on Analysis and Applications of Stochastic Systems
  • Place of Presentation: IMPA（ブラジル）
  • Year and Date: 2016-03-31
  • Int'l Joint Research / Invited
• [Presentation] 屈折反射レヴィー過程（特別講演） (2016)
  • Author(s): 山崎和俊
  • Organizer: 日本数学会
  • Place of Presentation: 筑波大学
  • Year and Date: 2016-03-16
  • Invited
• [Presentation] An Analytic Recursive Method for Optimal Multiple Stopping: Canadization and Phase-Type Fitting (2016)
  • Author(s): K. Yamazaki
  • Organizer: Winter Workshop on Operations Research, Finance and Mathematics, 2016
  • Place of Presentation: サホロリゾート（北海道）
  • Year and Date: 2016-02-15
  • Int'l Joint Research / Invited
• [Presentation] Refracted-Reflected Levy Processes in M/G/1 queues (2016)
  • Author(s): 山崎和俊
  • Organizer: 待ち行列シンポジウム
  • Place of Presentation: 多摩永山情報教育センター（東京）
  • Year and Date: 2016-01-21
• [Presentation] On the refracted-reflected spectrally one-sided Levy processes (2016)
  • Author(s): K. Yamazaki
  • Organizer: Levy 2016
  • Place of Presentation: フランス・Angers
  • Int'l Joint Research / Invited
• [Presentation] Parisian reflection and applications in insurance and credit risk (2016)
  • Author(s): K. Yamazaki
  • Organizer: International Conference on Financial Risks and Uncertainties
  • Place of Presentation: 沖縄
  • Int'l Joint Research / Invited
• [Presentation] パリジャン反射と保険・信用リスクへの応用 (2016)
  • Author(s): 山崎和俊
  • Organizer: 金融工学・数理計量ファイナンスの諸問題 2016
  • Place of Presentation: 大阪大学・中之島センター
  • Invited
• [Presentation] Optimality of Two-Parameter Strategies in Stochastic Control (2015)
  • Author(s): K. Yamazaki
  • Organizer: Simposio de Probabilidad y Procesos Estocasticos
  • Place of Presentation: Merida（メキシコ）
  • Year and Date: 2015-11-16
  • Int'l Joint Research / Invited
• [Presentation] Refracted-Reflected Spectrally Negative Levy Processes (2015)
  • Author(s): K. Yamazaki
  • Organizer: Workshop on Stochastic Analysis and Related Topics 2015
  • Place of Presentation: TU Dresden（ドイツ）
  • Year and Date: 2015-11-05
  • Int'l Joint Research
• [Presentation] Continuous-state branching processes (2015)
  • Author(s): K. Yamazaki
  • Organizer: Summer School on Dirichlet Forms and Stochastic Analysis
  • Place of Presentation: 関西大学
  • Year and Date: 2015-08-24
  • Int'l Joint Research
• [Presentation] Optimality of Refraction Strategies for Spectrally Negative Levy Processes (2015)
  • Author(s): K. Yamazaki
  • Organizer: Stochastic Processes and Applications Mongolia 2015
  • Place of Presentation: National University of Mongolia（モンゴル）
  • Year and Date: 2015-08-07
  • Int'l Joint Research
• [Presentation] Optimality of Refraction Strategies for Spectrally Negative Levy Processes (2015)
  • Author(s): K. Yamazaki
  • Organizer: Asian Quantitative Finance Conference
  • Place of Presentation: 香港中文大学（香港）
  • Year and Date: 2015-07-06
  • Int'l Joint Research / Invited
• [Presentation] レヴィー過程の確率制御 (2015)
  • Author(s): 山崎和俊
  • Organizer: 大規模複雑システムの最適モデリング手法の構築
  • Place of Presentation: 東京大学
  • Year and Date: 2015-06-02
  • Invited
• [Presentation] Optimality of Refraction Strategies for Spectrally Negative Levy Processes (2015)
  • Author(s): 山崎和俊
  • Organizer: 金融市場におけるシステミックリスクの学際的分析
  • Place of Presentation: 京都大学
  • Year and Date: 2015-05-29
  • Invited
• [Presentation] Optimality of Refraction Strategies for Spectrally Negative Levy Processes (2015)
  • Author(s): K. Yamazaki
  • Organizer: Insurance: Mathematics and Economics 2015
  • Place of Presentation: University of Liverpool（イギリス）
  • Year and Date: 2015-05-25
  • Int'l Joint Research
• [Presentation] Optimality of doubly reflected Levy processes in singular control (2015)
  • Author(s): K. Yamazaki
  • Organizer: Math Finance Seminar
  • Place of Presentation: Columbia University, U.S.A.
  • Year and Date: 2015-03-26
  • Invited
• [Presentation] Optimality of doubly reflected Levy processes in singular control (2015)
  • Author(s): K. Yamazaki
  • Organizer: ORFE Department Colloquium
  • Place of Presentation: Princeton University, U.S.A.
  • Year and Date: 2015-03-24
  • Invited
• [Presentation] Optimality of doubly reflected Levy processes in singular control (2015)
  • Author(s): K. Yamazaki
  • Organizer: Workshop on Mathematical Finance and Related Issues
  • Place of Presentation: Osaka University
  • Year and Date: 2015-03-19
  • Invited
• [Presentation] Optimal capital structure with scale effects under spectrally negative Levy models (2015)
  • Author(s): 山崎 和俊
  • Organizer: 日本応用数理学会 2015年 研究部会連合発表会
  • Place of Presentation: 明治大学
  • Year and Date: 2015-03-07
• [Presentation] Optimal capital structure with scale effects under spectrally negative Levy models (2014)
  • Author(s): K. Yamazaki
  • Organizer: SIAM Conference on Financial Mathematics and Engineering
  • Place of Presentation: Chicago, U.S.A.
  • Year and Date: 2014-11-13
• [Presentation] Inventory control for spectrally positive Levy demand processes (2014)
  • Author(s): K. Yamazaki
  • Organizer: INFORMS 2014
  • Place of Presentation: San Francisco, U.S.A.
  • Year and Date: 2014-11-12
• [Presentation] An analytic recursive method for optimal multiple stopping: Canadization and phase-type fitting (2014)
  • Author(s): 山崎 和俊
  • Organizer: 第４回数理ファイナンス合宿型セミナー
  • Place of Presentation: 慶応大学
  • Year and Date: 2014-11-08
  • Invited
• [Presentation] Cash management and control band policies for spectrally one-sided Levy processes (2014)
  • Author(s): K. Yamazaki
  • Organizer: TMU Finance Workshop 2014
  • Place of Presentation: 首都大学東京
  • Year and Date: 2014-11-07
  • Invited
• [Presentation] Phase-type approximation of the Gerber-Shiu function (2014)
  • Author(s): 山崎 和俊
  • Organizer: 日本保険・年金リスク学会 第12回大会
  • Place of Presentation: 東京大学
  • Year and Date: 2014-11-01
• [Presentation] 在庫管理問題の上向きジャンプ付レヴィー過程モデルへの一般化 (2014)
  • Author(s): 山崎 和俊
  • Organizer: 日本応用数理学会2014年度年会
  • Place of Presentation: 政策研究大学院大学
  • Year and Date: 2014-09-05
• [Presentation] Games of singular control and stopping driven by spectrally one-sided Levy processes (2014)
  • Author(s): K. Yamazaki
  • Organizer: The 37th Conference on Stochastic Processes and their Applications
  • Place of Presentation: Buenos Aires, Argentina
  • Year and Date: 2014-07-28
• [Presentation] Optimal dividends in the dual model under fixed transaction costs (2014)
  • Author(s): K. Yamazaki
  • Organizer: The 5th International Gerber-Shiu Workshop
  • Place of Presentation: The University of Hong Kong, Hong Kong
  • Year and Date: 2014-07-08
• [Presentation] Optimal dividends in the dual model under fixed transaction costs (2014)
  • Author(s): K. Yamazaki
  • Organizer: The 8th Samos Conference in Actuarial Science and Finance
  • Place of Presentation: Samos, Greece
  • Year and Date: 2014-05-31
• [Remarks] Kazutoshi Yamazaki
  • URL: https://sites.google.com/site/kyamazak/
• [Funded Workshop] 4th Asian Quantitative Finance Conference Osaka (2016)
  • Place of Presentation: 大阪大学中之島センター（大阪）
  • Year and Date: 2016-02-21