Maximum Principle for Near-Optimality of Mean-Field FBSDEs

Abstract EN

The present paper concerns with a near-optimal control problem for systems governed by mean-field forward-backward stochastic differential equations (FBSDEs) with mixed initial-terminal conditions.

Utilizing Ekeland’s variational principle as well as the reduction method, the necessary and sufficient near-optimality conditions are established in the form of Pontryagin’s type.

The results are obtained under restriction on the convexity of the control domain.

As an application, a linear-quadratic stochastic control problem is solved explicitly.