Extended mean-field control problem with partial observation

Recently, mean-filed games have become very popular subjects and the related McKean Vlasov type stochastic control problems have been widely studied. In view of the wide applications in finance and economics of extended mean-field control system, in this talk we investigate an extended mean-field control problem with partial observation, where the dynamic of the state is given by a forward-backward stochastic differential equation of McKean-Vlasov type. We first establish a necessary condition in the form of Pontryagin's maximum principle for optimality. Then a verification theorem is obtained for optimal control under some convex conditions of the Hamiltonian function. This talk is based on a joint work with Prof. Tianyang Nie.