The Maximum Principle of Forward Backward Transformation Stochastic Control System
Pure and Applied Mathematics Journal
Volume 4, Issue 3, June 2015, Pages: 109-114
Received: May 13, 2015;
Accepted: May 22, 2015;
Published: Jun. 1, 2015
Views 3302 Downloads 64
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
Follow on us
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.
Maximum Principle, Stochastic Control System, Forward Backward Transformation
To cite this article
The Maximum Principle of Forward Backward Transformation Stochastic Control System, Pure and Applied Mathematics Journal.
Vol. 4, No. 3,
2015, pp. 109-114.
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.
M. Tang and Q. Zhang, Optimal variational principle for backward stochastic control systems associated with Levy processes, Sci China Math, 55 (2012), 745-761.
SevaS. Tang and X. Li, Necessary condition for optimal control of stochastic systems with random jumps, SIAM J Control Optim, 32 (1994), 1447-1475.
J. Valero, On the kneser property for some parapolic problems, Topology and its applicanons, 155 (2005), 975-989.
Z. Wu, Maximum principle for optimal control problem of fully coupled forward-backward stochastic systems, J. Systems Sci. Math. Sci., 11 (1998), 249-259.
Z.Wu,Forward-backward stochastic differential equations with Brownian Motion and Process Poisson, Acta Math. Appl. Sinica, English Series, 15 (1999), 433-443.
Z. Wu, A maximum principle for partially observed optimal control of forward-backward stochastic control systems, Sci China Ser F, 53 (2010), 2205-2214.
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
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.
J. Xiong, An Introduction to Stochastic Filtering Theory, London, U.K.: Oxford University Press, 2008.