Maximum principles for forward-backward stochastic control systems with correlated state and observation noises. (English) Zbl 1262.93027
Summary: In this paper, we study a partial information optimal control problem derived by forward-backward stochastic systems with correlated noises between the system and the observation. Utilizing a direct method, an approximation method, and a Malliavin derivative method, we establish three versions of maximum principle (i.e., necessary condition) for optimal control. To show their applications, we work out two illustrative examples within the frameworks of linear-quadratic control and recursive utility and then solve them via the maximum principles and stochastic filtering.
MSC:
93E20 | Optimal stochastic control |
49K45 | Optimality conditions for problems involving randomness |
93E11 | Filtering in stochastic control theory |
60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
49N10 | Linear-quadratic optimal control problems |