Linear Quadratic Optimal Control Problems for Mean-Field Backward Stochastic Differential Equations

摘要

This paper is concerned with linear quadratic optimal control problems formean-field backward stochastic differential equations (MF-BSDEs, for short)with deterministic coefficients. The optimality system, which is a linearmean-field forward-backward stochastic differential equation with constraint,is obtained by a variational method. By decoupling the optimality system, twocoupled Riccati equations and an MF-BSDE are derived. It turns out that thecoupled two Riccati equations are uniquely solvable. Then a complete andexplicit representation is obtained for the optimal control.