The Maximum Principle of Forward Backward Transformation Stochastic Control System

Li Zhou; Hong Zhang; Jie Zhu; Shucong Ming

doi:doi:10.11648/j.pamj.20150403.18

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The Maximum Principle of Forward Backward Transformation Stochastic Control System

Li Zhou, Hong Zhang, Jie Zhu, Shucong Ming

Published in Pure and Applied Mathematics Journal (Volume 4, Issue 3)

Received: 13 May 2015 Accepted: 22 May 2015 Published: 1 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.

Published in	Pure and Applied Mathematics Journal (Volume 4, Issue 3)
DOI	10.11648/j.pamj.20150403.18
Page(s)	109-114
Creative Commons	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), 2015. Published by Science Publishing Group

Keywords

Maximum Principle, Stochastic Control System, Forward Backward Transformation

References

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[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.

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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://article.sciencepublishinggroup.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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TY  - JOUR
T1  - The Maximum Principle of Forward Backward Transformation Stochastic Control System
AU  - Li Zhou
AU  - Hong Zhang
AU  - Jie Zhu
AU  - Shucong Ming
Y1  - 2015/06/01
PY  - 2015
N1  - https://doi.org/10.11648/j.pamj.20150403.18
DO  - 10.11648/j.pamj.20150403.18
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 109
EP  - 114
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20150403.18
AB  - 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.
VL  - 4
IS  - 3
ER  -

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Author Information

Li Zhou

School of Information, Beijing Wuzi University, Beijing, China
Hong Zhang

School of Information, Beijing Wuzi University, Beijing, China
Jie Zhu

School of Information, Beijing Wuzi University, Beijing, China
Shucong Ming

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

Copy | Download

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

Copy | Download

@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://article.sciencepublishinggroup.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}
}

Copy | Download

TY  - JOUR
T1  - The Maximum Principle of Forward Backward Transformation Stochastic Control System
AU  - Li Zhou
AU  - Hong Zhang
AU  - Jie Zhu
AU  - Shucong Ming
Y1  - 2015/06/01
PY  - 2015
N1  - https://doi.org/10.11648/j.pamj.20150403.18
DO  - 10.11648/j.pamj.20150403.18
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 109
EP  - 114
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20150403.18
AB  - 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.
VL  - 4
IS  - 3
ER  -

Copy | Download