Mean-field stochastic linear quadratic optimal control problems: closed-loop solvability

作     者：Xun Li Jingrui Sun Jiongmin Yong 

作者机构：Department of Applied MathematicsThe Hong Kong Polytechnic UniversityHong KongChina Department of MathematicsUniversity of Central FloridaOrlandoFL 32816USA 

出 版 物：《Probability, Uncertainty and Quantitative Risk》 (概率、不确定性与定量风险（英文）)

年 卷 期：2016年第1卷第1期

页      面：37-60页

学科分类：07[理学] 0714[理学-统计学（可授理学、经济学学位）] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：supported by Hong Kong RGC under grants 519913,15209614 and 15224215 Jingrui Sun was partially supported by the National Natural Science Foundation of China(11401556) the Fundamental Research Funds for the Central Universities(WK 2040000012) Jiongmin Yong was partially supported by NSF DMS-1406776 

主　　题：Mean-field stochastic differential equation Linear quadratic optimal control Riccati equation Regular solution Closed-loop solvability 

摘      要：An optimal control problem is studied for a linear mean-field stochastic differential equation with a quadratic cost *** coefficients and the weighting matrices in the cost functional are all assumed to be *** strategies are introduced,which require to be independent of initial states;and such a nature makes it very useful and convenient in *** this paper,the existence of an optimal closed-loop strategy for the system(also called the closedloop solvability of the problem)is characterized by the existence of a regular solution to the coupled two(generalized)Riccati equations,together with some constraints on the adapted solution to a linear backward stochastic differential equation and a linear terminal value problem of an ordinary differential equation.