A Linear-Quadratic Optimal Control Problem for Mean-Field Stochastic Differential Equations

Details A Linear-Quadratic Optimal Control Problem for Mean-Field Stochastic Differential Equations A Linear-Quadratic Optimal Control Problem for Mean-Field Stochastic Differential Equations

2011-10-07

arxiv.org/abs/1110.1564v1

Mathematics

Optimization and Control

27 pages

Scientific paper

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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