A STOCHASTIC MAXIMUM PRINCIPLE FOR GENERAL MEAN-FIELD BACKWARD DOUBLY STOCHASTIC CONTROL

A STOCHASTIC MAXIMUM PRINCIPLE FOR GENERAL MEAN-FIELD BACKWARD DOUBLY STOCHASTIC CONTROL

S. AOUN, L. TAMER

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Abstract. In this paper we study the optimal control problems of general Mckean- Vlasov 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.

Keywords:Keywords: Backward doubly stochastic differential equations. Optimal control. McKean- Vlasov differential equations. Probability measure. Derivative with respect to measure.

AMS Subject Classification: 93E20, 60H10.