A new maximum principle for partially observed optimal control problems

This paper deals with partially observed optimal control of possibly degenerate stochastic differential equations, with correlated signal and observation noises. The control is allowed to enter into all the coefficients. Rather than going through a separated control problem, we consider instead the original problem directly, and present a new maximum principle (MP) for the partially observed optimal control, in which the adjoint processes are solutions to some finite-dimensional backward stochastic differential equations driven by both signal and observation noises. Alternative characterizations of the adjoint processes are given in terms of the observation-adapted vector fields, their differentials and Hessians, along the optimal signal process. The new MP is then connected with existing ones