Pure and Applied Mathematics Journal

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The Maximum Principle of Forward Backward Transformation Stochastic Control System

Received: 13 May 2015    Accepted: 22 May 2015    Published: 01 June 2015
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Abstract

In the paper, we discuss the maximum principle for the forward backward stochastic system. Assume the system follows a coupled forward backward stochastic differential equation modulated by a Marlcov chain and the control domain is convex. By convex variable method, we give the necessary and sufficient conditions for the existence of optimal control.

DOI 10.11648/j.pamj.20150403.18
Published in Pure and Applied Mathematics Journal (Volume 4, Issue 3, June 2015)
Page(s) 109-114
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This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Maximum Principle, Stochastic Control System, Forward Backward Transformation

References
[1] A. Szukala, A Knese-type theorem for euqation x=f (t, x) in locally convex spaces, Journal for analysis and its applications, 18 (1999), 1101-1106.
[2] M. Tang and Q. Zhang, Optimal variational principle for backward stochastic control systems associated with Levy processes, Sci China Math, 55 (2012), 745-761.
[3] SevaS. Tang and X. Li, Necessary condition for optimal control of stochastic systems with random jumps, SIAM J Control Optim, 32 (1994), 1447-1475.
[4] J. Valero, On the kneser property for some parapolic problems, Topology and its applicanons, 155 (2005), 975-989.
[5] Z. Wu, Maximum principle for optimal control problem of fully coupled forward-backward stochastic systems, J. Systems Sci. Math. Sci., 11 (1998), 249-259.
[6] Z.Wu,Forward-backward stochastic differential equations with Brownian Motion and Process Poisson, Acta Math. Appl. Sinica, English Series, 15 (1999), 433-443.
[7] Z. Wu, A maximum principle for partially observed optimal control of forward-backward stochastic control systems, Sci China Ser F, 53 (2010), 2205-2214.
[8] Z.Wu and Z. Yu,Fully coupled forward-backward stochastic differential equations and related partial differential equations system, Chinese Ann Math Ser A, 25 (2004), 457-468
[9] H. Xiao and G. Wang, A necessary condition for optimal control of initial coupled forward-backward stochastic differential equations with partial information, J. Appl. Math. Comput., 37 (2011), 347-359.
[10] J. Xiong, An Introduction to Stochastic Filtering Theory, London, U.K.: Oxford University Press, 2008.
Author Information
  • School of Information, Beijing Wuzi University, Beijing, China

  • School of Information, Beijing Wuzi University, Beijing, China

  • School of Information, Beijing Wuzi University, Beijing, China

  • Chinese Academy of Finance and Development, Central University of Finance and Economics, Beijing, China

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  • APA Style

    Li Zhou, Hong Zhang, Jie Zhu, Shucong Ming. (2015). The Maximum Principle of Forward Backward Transformation Stochastic Control System. Pure and Applied Mathematics Journal, 4(3), 109-114. https://doi.org/10.11648/j.pamj.20150403.18

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    ACS Style

    Li Zhou; Hong Zhang; Jie Zhu; Shucong Ming. The Maximum Principle of Forward Backward Transformation Stochastic Control System. Pure Appl. Math. J. 2015, 4(3), 109-114. doi: 10.11648/j.pamj.20150403.18

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    AMA Style

    Li Zhou, Hong Zhang, Jie Zhu, Shucong Ming. The Maximum Principle of Forward Backward Transformation Stochastic Control System. Pure Appl Math J. 2015;4(3):109-114. doi: 10.11648/j.pamj.20150403.18

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  • @article{10.11648/j.pamj.20150403.18,
      author = {Li Zhou and Hong Zhang and Jie Zhu and Shucong Ming},
      title = {The Maximum Principle of Forward Backward Transformation Stochastic Control System},
      journal = {Pure and Applied Mathematics Journal},
      volume = {4},
      number = {3},
      pages = {109-114},
      doi = {10.11648/j.pamj.20150403.18},
      url = {https://doi.org/10.11648/j.pamj.20150403.18},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.pamj.20150403.18},
      abstract = {In the paper, we discuss the maximum principle for the forward backward stochastic system. Assume the system follows a coupled forward backward stochastic differential equation modulated by a Marlcov chain and the control domain is convex. By convex variable method, we give the necessary and sufficient conditions for the existence of optimal control.},
     year = {2015}
    }
    

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    AU  - Shucong Ming
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