A Linear-Quadratic Optimal Control Problem for Mean-Field Stochastic Differential Equations
Optimization and Control
2011-10-10 v1 Probability
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.
Cite
@article{arxiv.1110.1564,
title = {A Linear-Quadratic Optimal Control Problem for Mean-Field Stochastic Differential Equations},
author = {Jiongmin Yong},
journal= {arXiv preprint arXiv:1110.1564},
year = {2011}
}
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27 pages