Maximum principle for forward-backward partially observed optimal control of stochastic systems with delay

Abstract

In this paper, we consider partially observed optimal control for forward-backward stochastic delay differential equations (FBSDDEs) where the control domain is non-convex and the control variable is allowed to enter into both diffusion and observation terms. We obtain a general stochastic maximum principle of these optimal control problems by using Girsanov’s theorem, the spike variational method and the filtering technique. We also derive the adjoint equations to the problem. Finally, we apply our results to study a linear-quadratic (LQ) optimal control with delay.