A GENERAL STOCHASTIC MAXIMUM PRINCIPLE FOR A MARKOV REGIME SWITCHING JUMP-DIFFUSION MODEL OF MEAN-FIELD TYPE

被引：30

作者：

Zhang, Xin ^{[1
]}

Sun, Zhongyang ^{[2
]}

Xiong, Jie ^{[3
]}

机构：

[1] Southeast Univ, Sch Math, Nanjing 211189, Jiangsu, Peoples R China

[2] Qufu Normal Univ, Sch Stat, Qufu 273165, Shandong, Peoples R China

[3] Southern Univ Sci & Technol, Dept Math, Shenzhen 518055, Peoples R China

来源：

SIAM JOURNAL ON CONTROL AND OPTIMIZATION | 2018年 / 56卷 / 04期

基金：

中国国家自然科学基金; 中国博士后科学基金;

关键词：

stochastic maximum principle; regime switching; mean-field type model; jump-diffusion mean-field BSDE; linear quadratic control problem; SYSTEM;

D O I：

10.1137/17M112395X

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

In this paper, we develop a global form stochastic maximum principle for a Markov regime switching mean-field model driven by Brownian motions and Poisson jumps. The form of the maximum principle turns out to be quite different from the classical one in the sense that here the first order adjoint process is defined as a solution to a certain jump-diffusion mean-field backward stochastic differential equation (BSDE), but the second order adjoint equation is still a classical BSDE. As an application, we apply the main results to study a linear quadratic stochastic control problem of mean-field type.

引用

页码：2563 / 2592

页数：30

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