A Stochastic Maximum Principle for Partially Observed Optimal Control Problem of Mckean-Vlasov FBSDEs with Random Jumps

In this paper, we study the stochastic maximum principle for partially observed optimal control problem of forward-backward stochastic differential equations of McKean-Vlasov type driven by a Poisson random measure and an independent Brownian motion. The coefficients of the system and the cost functional depend on the state of the solution process as well as of its probability law and the control variable. Necessary and sufficient conditions of optimality for this systems are established under assumption that the control domain is supposed to be convex. Our main result is based on Girsavov's theorem and the derivatives with respect to probability law. As an illustration, a partially observed linear-quadratic control problem of McKean-Vlasov forward-backward stochastic differential equations type is studied in terms of the stochastic filtering.