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2012 Fiscal Year Final Research Report

Stochastic control of Levy driven processes with application to mathematical finance

Research Project

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Project/Area Number 21686039
Research Category

Grant-in-Aid for Young Scientists (A)

Allocation TypeSingle-year Grants
Research Field Control engineering
Research InstitutionOsaka 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

    (14 results)

All 2013 2012 2011 2010 2009 Other

All Journal Article (6 results) (of which Peer Reviewed: 6 results) Presentation (6 results) Remarks (2 results)

  • [Journal Article] On weak approximation of stochastic differential equations through hard bounds by mathematical programming2013

    • 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 dynamics2011

    • 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 optimization2011

    • 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 jumps2011

    • 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 equation2012

    • 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 robustness2011

    • 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 models2011

    • 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 Formula2010

    • 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 pricing2009

    • 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

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Published: 2014-08-29  

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