A maximum principle for partially observed optimal control of forward-backward stochastic control systems

This paper studies an optimal control problem for partially observed forward-backward stochastic control system with a convex control domain and the forward diffusion term containing control variable. A maximum principle is proved for this kind of partially observable optimal control problems and the corresponding adjoint processes are characterized by the solutions of certain forward-backward stochastic differential equations in finite-dimensional spaces. One partially observed recursive linear-quadratic (LQ) optimal control example is also given to show the application of the obtained maximum principle. An explicit observable optimal control is obtained in this example.

[1]  X. Zhou.  On the necessary conditions of optimal controls for stochastic partial differential equations , 1993 .

[2]  Jie Xiong,et al.  An Introduction to Stochastic Filtering Theory , 2008 .

[3]  XiaoPeng Liu,et al.  The generalization of a class of impulse stochastic control models of a geometric Brownian motion , 2009, Science in China Series F: Information Sciences.

[4]  Xunjing Li,et al.  Necessary Conditions for Optimal Control of Stochastic Systems with Random Jumps , 1994 .

[5]  X. Zhou,et al.  Stochastic Controls: Hamiltonian Systems and HJB Equations , 1999 .

[6]  J. Lepeltier,et al.  Zero-sum stochastic differential games and backward equations , 1995 .

[7]  Hai-ping Shi.  Backward stochastic differential equations in finance , 2010 .

[8]  Larry G. Epstein,et al.  Stochastic differential utility , 1992 .

[9]  R. Elliott,et al.  The partially observed stochastic minimum principle , 1989 .

[10]  Alain Bensoussan,et al.  Maximum principle and dynamic programming approaches of the optimal control of partially observed diffusions , 1983 .

[11]  Ulrich G. Haussmann,et al.  The maximum principle for optimal control of diffusions with partial information , 1987 .

[12]  S. Peng,et al.  Adapted solution of a backward stochastic differential equation , 1990 .

[13]  S. Peng.  A general stochastic maximum principle for optimal control problems , 1990 .

[14]  Wendell H. Fleming,et al.  Optimal Control of Partially Observable Diffusions , 1968 .

[15]  N. Williams.  On Dynamic Principal-Agent Problems in Continuous Time , 2004 .

[16]  W. Wonham.  On the Separation Theorem of Stochastic Control , 1968 .

[17]  S. Peng,et al.  Fully Coupled Forward-Backward Stochastic Differential Equations and Applications to Optimal Control , 1999 .

[18]  Shi,et al.  The Maximum Principle for Fully Coupled Forward-backward Stochastic Control System , 2006 .

[19]  Shanjian Tang,et al.  The Maximum Principle for Partially Observed Optimal Control of Stochastic Differential Equations , 1998 .