SIAM Journal on Control and Optimization, Vol.51, No.4, 2809-2838, 2013
LINEAR-QUADRATIC OPTIMAL CONTROL PROBLEMS FOR MEAN-FIELD STOCHASTIC DIFFERENTIAL EQUATIONS
Linear-quadratic optimal control problems are considered for mean-field stochastic differential equations with deterministic coefficients. By a variational method, the optimality system is derived, which is 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.
Keywords:mean-field stochastic differential equation;linear-quadratic optimal control;Riccati differential equation;feedback representation