Abstract
A Linear-quadratic optimal control problem is considered for mean-field stochastic differential equations with deterministic coefficients. By a variational method, the optimality system is derived, which turns out to be a linear mean-field forward-backward stochastic differential equation. Using a decoupling technique, two Riccati differential equations are obtained, which are uniquely solvable under certain conditions. Then a feedback representation is obtained for the optimal control.
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