Linear-Quadratic Delayed Mean-Field Social Optimization

被引：1

作者：

Nie, Tianyang ^{[1
]}

Wang, Shujun ^{[2
]}

Wu, Zhen ^{[1
]}

机构：

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

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

来源：

APPLIED MATHEMATICS AND OPTIMIZATION | 2024年 / 89卷 / 01期

基金：

国家重点研发计划; 中国国家自然科学基金;

关键词：

Asymptotic social optima; Delayed person-by-person optimality; Discrete-type heterogeneous system; Mean-field type AFBSDDE; LQ control; Mean-field team with delay; STOCHASTIC DIFFERENTIAL-EQUATIONS; MAXIMUM PRINCIPLE; SYSTEMS; GAME; OPTIMA;

D O I：

10.1007/s00245-023-10067-5

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A linear quadratic (LQ) stochastic optimization problem with delay involving weakly-coupled large population is investigated in this paper. Different to classic mean field (MF) game, here agents cooperate with each other to minimize the so-called social objective. With the aid of delayed person-by-person optimality principle, one arrives at an auxiliary LQ delayed control problem by decentralized information. A decentralized strategy is obtained by feat of an MF type anticipated forward-backward stochastic differential delay equation (AFBSDDE) consistency condition. The discounting method with delay feature is employed to solve the consistency condition system. Finally, by some estimates of AFBSDDEs we derive the asymptotic social optimality.

引用

页数：43

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