A stochastic maximum principle for general mean-field backward doubly stochastic control

Abstract

In this paper we study the optimal control problems of general MckeanVlasov for backward doubly stochastic differential equations (BDSDEs), in which the coefficients depend on the state of the solution process as well as of its law. We establish a stochastic maximum principle on the hypothesis that the control field is convex. For example, an example of a control problem is offered and solved using the primary result.