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

被引：0
作者：
Qingfeng Zhu
Lijiao Su
Fuguo Liu
Yufeng Shi
Yong’ao Shen
Shuyang Wang
机构：
[1] Shandong University of Finance and Economics,School of Mathematics and Quantitative Economics
[2] and Shandong Key Laboratory of Blockchain Finance,Institute for Financial Studies and School of Mathematics
[3] Shandong University,Department of Mathematics
[4] Changji University,School of Informatics
[5] Xiamen University,undefined
来源：
Frontiers of Mathematics in China | 2020年 / 15卷
关键词：
Non-zero sum stochastic differential game; mean-field; backward doubly stochastic differential equation (BDSDE); Nash equilibrium point; maximum principle; 60H10; 91A15; 49N10;
D O I：
暂无
中图分类号：
学科分类号：
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.
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页码：1307 / 1326
页数：19
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