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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.

Keywords

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}
}

Comments

27 pages

R2 v1 2026-06-21T19:16:47.017Z