A Type of General Forward-Backward Stochastic Differential Equations and Applications  

作　　者：Li CHEN Zhen WU 

机构地区：[1]Department of Mathematics, China University of Mining and Technology, Beijing 100083, China [2]Corresponding author. School of Mathematics, Shandong University, Jinan 250100, China

出　　处：《Chinese Annals of Mathematics,Series B》2011年第2期279-292,共14页数学年刊（B辑英文版）

基　　金：Project supported by the 973 National Basic Research Program of China (No. 2007CB814904);the National Natural Science Foundations of China (No. 10921101);the Shandong Provincial Natural Science Foundation of China (No. 2008BS01024);the Science Fund for Distinguished Young Scholars of Shandong Province (No. JQ200801);the Shandong University Science Fund for Distinguished Young Scholars(No. 2009JQ004)

摘　　要：The authors discuss one type of general forward-backward stochastic differential equations (FBSDEs) with Ito's stochastic delayed equations as the forward equations and anticipated backward stochastic differential equations as the backward equations.The existence and uniqueness results of the general FBSDEs are obtained.In the framework of the general FBSDEs in this paper,the explicit form of the optimal control for linear-quadratic stochastic optimal control problem with delay and the Nash equilibrium point for nonzero sum differential games problem with delay are obtained.

关 键 词：Stochastic delayed differential equations Anticipated backward stochastic differential equations Forward-backward stochastic differential equations Linear-quadratic stochastic optimal control with delay Nonzero sum stochastic differential game with delay 

分 类 号：O211.63[理学—概率论与数理统计] TP316[理学—数学]