Fully Coupled Forward-Backward Stochastic Functional Differential Equations and Applications to Quadratic Optimal Control  

作　　者：XU Xiaoming 

机构地区：[1]Institute of Finance and Statistics,School of Mathematical Sciences,Nanjing Normal University,Nanjing210023,China

出　　处：《Journal of Systems Science & Complexity》2020年第6期1886-1902,共17页系统科学与复杂性学报（英文版）

基　　金：the Program of Natural Science Research of Jiangsu Higher Education Institutions of China under Grant No. 17KJB110009。

摘　　要：This paper considers the fully coupled forward-backward stochastic functional differential equations(FBSFDEs) with stochastic functional differential equations as the forward equations and the generalized anticipated backward stochastic differential equations as the backward equations. The authors will prove the existence and uniqueness theorem for FBSFDEs. As an application, we deal with a quadratic optimal control problem for functional stochastic systems, and get the explicit form of the optimal control by virtue of FBSFDEs.

关 键 词：Forward-backward stochastic functional differential equation functional stochastic system generalized anticipated backward stochastic differential equation quadratic optimal control stochastic functional differential equation 

分 类 号：O232[理学—运筹学与控制论] O211.63[理学—数学]