Linear Quadratic Leader-Follower Stochastic Differential Games:Closed-Loop Solvability  

作　　者：LI Zixuan SHI Jingtao 

机构地区：[1]School of Mathematics,Shandong University,Jinan 250100,China

出　　处：《Journal of Systems Science & Complexity》2023年第4期1373-1406,共34页系统科学与复杂性学报（英文版）

基　　金：This work was supported by National Key Research&Development Program of China under Grant No.2022YFA1006104;National Natural Science Foundations of China under Grant Nos.11971266,11831010;Shandong Provincial Natural Science Foundations under Grant Nos.ZR2022JQ01,ZR2020ZD24,ZR2019ZD42.

摘　　要：In this paper,a leader-follower stochastic differential game is studied for a linear stochastic differential equation with quadratic cost functionals.The coefficients in the state equation and the weighting matrices in the cost functionals are all deterministic.Closed-loop strategies are introduced,which require to be independent of initial states;and such a nature makes it very useful and convenient in applications.The follower first solves a stochastic linear quadratic optimal control problem,and his optimal closed-loop strategy is characterized by a Riccati equation,together with an adapted solution to a linear backward stochastic differential equation.Then the leader turns to solve a stochastic linear quadratic optimal control problem of a forward-backward stochastic differential equation,necessary conditions for the existence of the optimal closed-loop strategy for the leader is given by a Riccati equation.Some examples are also given.

关 键 词：Backward stochastic differential equation closed-loop solvability leader-follower stochastic differential game linear quadratic control Riccati equation Stackelberg equilibrium 

分 类 号：O211.63[理学—概率论与数理统计] O232[理学—数学]