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.
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