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

作　　者：Qingfeng ZHU Lijiao SU Fuguo LIU Yufeng SHI Yong’ao SHEN Shuyang WANG 

机构地区：[1]School of Mathematics and Quantitative Economics,Shandong University of Finance and Economics,and Shandong Key Laboratory of Blockchain Finance,Jinan 250014,China [2]Institute for Financial Studies and School of Mathematics,Shandong University,Jinan 250100,China [3]Department of Mathematics,Changji University,Changji 831100,China [4]School of Informatics,Xiamen University,Xiamen 361005,China

出　　处：《Frontiers of Mathematics in China》2020年第6期1307-1326,共20页中国高等学校学术文摘·数学（英文）

基　　金：supported in part by the National Natural Science Foundation of China(Grant Nos.11871309,11671229,71871129,11371226,11301298);the National Key R&D Program of China(Grant No.2018 YFA0703900);the Natural Science Foundation of Shandong Province(No.ZR2019MA013);the Special Funds of Taishan Scholar Project(No.tsqn20161041);the Fostering Project of Dominant Discipline and Talent Team of Shandong Province Higher Education Institutions.

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.

关 键 词：Non-zero sum stochastic differential game mean field backward doubly stochastic differential equation(BDSDE) Nash equilibrium point maximum principle 

分 类 号：O211.63[理学—概率论与数理统计]