Mean-field type forward-backward doubly stochastic differential equations and related stochastic differential games

被引：3

作者：

Zhu, Qingfeng ^{[1
,2
,3
,4
]}

Su, Lijiao ^{[1
,2
]}

Liu, Fuguo ^{[5
]}

Shi, Yufeng ^{[3
,4
]}

Shen, Yong'ao ^{[1
,2
]}

Wang, Shuyang ^{[6
]}

机构：

[1] Shandong Univ Finance & Econ, Sch Math & Quantitat Econ, Jinan 250014, Peoples R China

[2] Shandong Key Lab Blockchain Finance, Jinan 250014, Peoples R China

[3] Shandong Univ, Inst Financial Studies, Jinan 250100, Peoples R China

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

[5] Changji Univ, Dept Math, Changji 831100, Peoples R China

[6] Xiamen Univ, Sch Informat, Xiamen 361005, Peoples R China

来源：

FRONTIERS OF MATHEMATICS IN CHINA | 2020年 / 15卷 / 06期

基金：

中国国家自然科学基金; 国家重点研发计划;

关键词：

Non-zero sum stochastic differential game; mean-field; backward doubly stochastic differential equation (BDSDE); Nash equilibrium point; maximum principle; MAXIMUM PRINCIPLE; CONTROL SYSTEMS;

D O I：

10.1007/s11464-020-0889-y

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study a kind of partial information non-zero sum differential games of mean-field backward doubly stochastic differential equations, in which the coefficient contains not only the state process but also its marginal distribution, and the cost functional is also of mean-field type. It is required that the control is adapted to a sub-filtration of the filtration generated by the underlying Brownian motions. We establish a necessary condition in the form of maximum principle and a verification theorem, which is a sufficient condition for Nash equilibrium point. We use the theoretical results to deal with a partial information linear-quadratic (LQ) game, and obtain the unique Nash equilibrium point for our LQ game problem by virtue of the unique solvability of mean-field forward-backward doubly stochastic differential equation.

引用

页码：1307 / 1326

页数：20

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