Optimal Control of FBSDE with Partially Observable Information

In this chapter, we study an optimal control problem with state process governed by a nonlinear FBSDE and with partially observable information, i.e., Problem B introduced in Section  1.2. For simplicity, we take the dimensions n=m=k=k~=1n=m=k=k~=1. Using a direct method and a Malliavin derivative method, we establish two versions of the stochastic maximum principle for the characterization of the optimal control. To demonstrate the applicability, we work out an illustrative example within the framework of recursive utility and then solve it via the stochastic maximum principle and the stochastic filtering.