A closed-loop saddle point for zero-sum linear-quadratic stochastic differential games with mean-field type

被引：17

作者：

Tian, Ran ^{[1
]}

Yu, Zhiyong ^{[2
]}

Zhang, Rucheng ^{[1
]}

机构：

[1] Shandong Univ, Zhongtai Secur Inst Financial Studies, Jinan 250100, Shandong, Peoples R China

[2] Shandong Univ, Sch Math, Jinan 250100, Shandong, Peoples R China

来源：

SYSTEMS & CONTROL LETTERS | 2020年 / 136卷

基金：

国家重点研发计划; 中国国家自然科学基金;

关键词：

Stochastic linear-quadratic problem; Mean-field type stochastic differential equation; Stochastic differential game; Closed-loop representation; Riccati differential equation; VISCOSITY SOLUTIONS; EQUATIONS;

D O I：

10.1016/j.sysconle.2020.104624

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

This paper is concerned with a linear-quadratic zero-sum differential game with mean-field type. The notions of explicit and implicit strategy laws are proposed. Based on them, a closed-loop formulation for saddle points in the mixed-strategy-law form is established. In order to construct the saddle point, the classical entire completion-of-square argument is developed to a four-step-completion-of-square argument, and a pair of optimality conditions is proposed. (C) 2020 Elsevier B.V. All rights reserved.

引用

页数：11

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