Optimal control of mean-field jump-diffusion systems with delay: A stochastic maximum principle approach

被引：46

作者：

Meng, Qingxin ^{[1
]}

Shen, Yang ^{[2
,3
]}

机构：

[1] Huzhou Univ, Dept Math Sci, Huzhou 313000, Zhejiang, Peoples R China

[2] Univ New S Wales, Business Sch, Sch Risk & Actuarial Studies, Sydney, NSW 2052, Australia

[3] Univ New S Wales, Business Sch, CEPAR, Sydney, NSW 2052, Australia

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2015年 / 279卷

基金：

中国博士后科学基金; 中国国家自然科学基金;

关键词：

Mean-field; Stochastic delay differential equation; Advanced backward stochastic differential equation; Optimal control; Stochastic maximum principle; DIFFERENTIAL-EQUATIONS; FINANCE; MODEL;

D O I：

10.1016/j.cam.2014.10.011

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper is concerned with an optimal control problem under mean-field jump-diffusion systems with delay. Firstly, some existence and uniqueness results are proved for a jump-diffusion mean-field stochastic delay differential equation and a jump-diffusion mean-field advanced backward stochastic differential equation. Then necessary and sufficient maximum principles for control systems of mean-field type and with delay are established under certain conditions. A mean-field, delayed, linear-quadratic control problem is finally discussed using the obtained maximum principles. (C) 2014 Elsevier B.V. All rights reserved.

引用

页码：13 / 30

页数：18

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