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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
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