A NECESSARY CONDITION FOR MEAN-FIELD TYPE STOCHASTIC DIFFERENTIAL EQUATIONS WITH CORRELATED STATE AND OBSERVATION NOISES.

This paper is concerned with a mean-field type optimal control problem, whose new features are that the state x_t^v is partially observed by a noisy process y(t), and the control problem is time inconsistent in the sense that Bellman optimality principle does not work. A necessary condition for optimality is derived by convex variation, dual technique and backward stochastic differential equations (BSDEs). A linear-quadratic (LQ) optimal control example is studied, and the optimal solution is obtained by the optimal filtering for BSDEs and the necessary condition. [ABSTRACT FROM AUTHOR]