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

2011/10/07 by Jiongmin Yong, Yong, Jiongmin · 3 citations
Economics, Econometrics and Finance · Engineering · #49N10 #49N35 #93E20 #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Optimization and Control (math.OC) #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1110.1564

openalex publication_date 2011/10/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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