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Linear Quadratic Leader-Follower Stochastic Differential Games:closed-loop solvability

系统科学与复杂性学报:英文版 2023年第4期36卷 1373-1406页

作者： LI Zixuan SHI Jingtao School of Mathematics Shandong UniversityJinan 250100China

In this paper,a leader-follower stochastic differential game is studied for a linear stochastic differential equation with quadratic cost *** coefficients in the state equation and the weighting matrices in the cost functionals are all ***-loop strategies are introduced,which require to be independent of initial states;and such a nature makes it very useful and convenient in *** 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 *** 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 *** 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

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

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Probability, Uncertainty and Quantitative Risk 2016年第1期1卷 37-60页

作者： Xun Li Jingrui Sun Jiongmin Yong Department of Applied Mathematics The Hong Kong Polytechnic UniversityHong KongChina Department of Mathematics University of Central FloridaOrlandoFL 32816USA

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.

关键词： Mean-field stochastic differential equation Linear quadratic optimal control Riccati equation Regular solution closed-loop solvability

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Linear Quadratic Stackelberg Stochastic Differential Games:closed-loop solvability

Linear Quadratic Stackelberg Stochastic Differential Games:C...

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第40届中国控制会议

作者： Zixuan Li Jingtao Shi School of Mathematics Shandong University

This paper is concerned with the closed-loop solvability of one kind of linear-quadratic Stackelberg stochastic differential game, where the coefficients are deterministic. The notion of the closed-loop solvability is introduced, which require to be independent of the initial state. The follower’s problem is solved first, and the closed-loop optimal strategy is characterized by a Riccati equation, together with an adapted solution to a linear backward stochastic differential equation. Then the necessary conditions of the existence of the leader’s nonanticipating closed-loop optimal strategy is obtained via a system of cross-coupled Riccati equations. The sufficiency is open since the completion-of-square method is invalid.

关键词： Stackelberg stochastic differential game closed-loop solvability linear quadratic control forward-backward stochastic differential equation Riccati equation

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