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