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International Journal of Control, Vol.92, No.10, 2463-2472, 2019
The maximum principle for partially observed optimal control problems of mean-field FBSDEs
This paper is concerned with a partially observed optimal control problem described by mean-field forward and backward stochastic differential equations. Moreover, the control variable enters the diffusion coefficient and the control domain is non-convex. Utilising Girsanov's theorem as well as extended Ekeland's variational principle, a maximum principle is established in the form of Pontryagin's type. As an application, a linear-quadratic control problem is studied in terms of the stochastic filtering.
Keywords:Mean-field SDE;Girsanov's theorem;extended Ekeland's variational principle;maximum principle;stochastic filtering