The maximum principle for partially observed optimal control of fully coupled forward-backward stochastic systems with state constraints

This paper is concerned with partially observed stochastic optimal control problems for fully coupled forward-backward stochastic systems with state constraints. The maximum principle is obtained in global form under the assumption that the forward diffusion coefficient does not contain the control variable and the control domain is not necessarily convex. By Ekeland´s variational principle, a classical spike variational method in the study of completely observed case together with a pure probabilistic filtering technique is used, and the related adjoint processes are characterized as solutions to related forward-backward stochastic differential equations in finite-dimensional spaces.