Stochastic control of Levy driven processes with application to mathematical finance

2012 Fiscal Year Final Research Report

• Project/Area Number: 21686039
• Research Category: Grant-in-Aid for Young Scientists (A)
• Allocation Type: Single-year Grants
• Research Field: Control engineering
• Research Institution: Osaka University (2011-2012); Tokyo Institute of Technology (2009-2010)
• Principal Investigator: KASHIMA Kenji 大阪大学, 基礎工学研究科, 准教授 (60401551)
• Research Collaborator: KAWAI Reiichiro 英国・レスター大学, 数学科 ; IMURA Jun-ichi 東京工業大学, 情報理工学研究科, 教授
• Project Period (FY): 2009 – 2012
• Keywords: 確率制御 / レヴィ過程 / 数理ファイナンス / システムバイオロジ / 最適化 / 大規模複雑系

Research Abstract

We proposed an optimization approach to weak approximation of Levy-driven stochastic differential equations, which is a general form of many practical applications. We employ a mathematical programming framework to obtain numerically upper and lower bound estimates of the target. An advantage of our approach is that we do need no sample path generation. The effectiveness was verified through an application to mathematical finance. We also investigated analysis/design of stochastic control systems from various aspects, such as robustness of consensus dynamics overlarge-scale complex networks under stochastic noise.

Research Products

• [Journal Article] On weak approximation of stochastic differential equations through hard bounds by mathematical programming (2013)
  • Author(s): Kenji Kashima, Reiichiro Kawai
  • Journal Title: SIAM Journal on Scientific Computing Volume: Vol. 35, Issue 1 Pages: A1/A21
  • Peer Reviewed
• [Journal Article] サンプル値 H^2信号復元にもとづくレビー過程の弱近似 (2011)
  • Author(s): 加嶋健司
  • Journal Title: システム制御情報学会論文誌 Volume: Vol. 24, Issue 10 Pages: 241/249
  • Peer Reviewed
• [Journal Article] Oscillation analysis of linearly coupled piecewise affine systems: application to spatio-temporal neuron dynamics (2011)
  • Author(s): Kenji Kashima, Yasuyuki Kawamura, Jun-ichi Imura
  • Journal Title: Automatica Volume: Vol. 47, Issue 6 Pages: 1249/1254
  • Peer Reviewed
• [Journal Article] A weak approximation of stochastic differential equations with jumps through tempered polynomial optimization (2011)
  • Author(s): Kenji Kashima, Reiichiro Kawai
  • Journal Title: Stochastic Models Volume: Vol. 27, Issue 1 Pages: 26/49
  • Peer Reviewed
• [Journal Article] An optimization approach to weak approximation of stochastic differential equations with jumps (2011)
  • Author(s): Kenji Kashima, Reiichiro Kawai
  • Journal Title: Applied Numerical Mathematics Volume: Vol. 61, Issue 5 Pages: 641/650
  • Peer Reviewed
• [Journal Article] On the convergence rate of diffusion in the bidirectional Erdos-Renyi networks: an H2-norm perspective
  • Author(s): Kenji Kashima, Yutaka Takahashi, Jun-ichi Imura
  • Journal Title: Physica A
  • Peer Reviewed
• [Presentation] Clustering-based H2-state aggregation of positive networks and its application to reduction of chemical master equation (2012)
  • Author(s): Takayuki Ishizaki, Kenji Kashima, Antoine Girard, Jun-ichi Imura, Luonan Chen, Kauzyuki Aihara
  • Organizer: 51th IEEE Conf. Decision and Control (CDC), pp. 4175/4180
  • Year and Date: 20120000
• [Presentation] 動的システムの空間構造:均質性とスケーラビリティ (2012)
  • Author(s): 加嶋健司
  • Organizer: 第12回制御部門大会,パイオニア賞受賞記念講演
  • Place of Presentation: 奈良
  • Year and Date: 20120000
• [Presentation] A linear multi-agent systems approach to diffusively coupled piecewise affine systems: delay robustness (2011)
  • Author(s): Kenji Kashima, Antonis Papachristodoulou, Frank Allgower
  • Organizer: 2011 IEEE Conf. Decision and Control (CDC), pp. 603/608
  • Year and Date: 20110000
• [Presentation] Connection profile robustness in a heterogeneous network of piecewise affine FitzHugh-Nagumo models (2011)
  • Author(s): Kenji Kashima, Antonis Papachristodoulou, Frank Allgower
  • Organizer: SICE Annual Conf. 2011, pp. 2093/2098
  • Year and Date: 20110000
• [Presentation] Smith-Predictor type Structure for a Class of Infinite-Dimensional Systems: Optimal Control and Performance Limitation Formula (2010)
  • Author(s): Kenji Kashima
  • Organizer: Semi-Plenary Talk in 19th. Int'l Symp. on Mathematical Theory of Networks and Systems (MTNSSemi-Plenary Talk in 19th. Int'l Symp. on Mathematical Theory of Networks and Systems (MTNSSemi-Plenary Talk in 19th. Int'l Symp. on Mathematical Theory of Networks
  • Place of Presentation: Budapest, Hungary
  • Year and Date: 20100000
• [Presentation] An optimization approach to weak approximation of Levy-driven stochastic differential equations with application to option pricing (2009)
  • Author(s): Kenji Kashima, Reiichiro Kawai
  • Organizer: 48th IEEE Conf. Decision and Control (CDC), 3673/3678
  • Year and Date: 20090000
• [Remarks] (1) 大木健太郎,加嶋健司"確率的な現象とその多様な捉え方,"計測と制御, 採録決定, 2013
• [Remarks] (2) 加嶋健司,河合玲一郎"レビー過程 - 白色雑音の一般化,"システム / 制御 / 情報, Vol. 55, Issue 12, pp. 505/512, 2011