Frontiers of Mathematics in China >
Mean-field type forward-backward doubly stochastic differential equations and related stochastic differential games
Received date: 18 Feb 2019
Accepted date: 18 Dec 2020
Published date: 15 Dec 2020
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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.
Qingfeng ZHU , Lijiao SU , Fuguo LIU , Yufeng SHI , Yong’ao SHEN , Shuyang WANG . Mean-field type forward-backward doubly stochastic differential equations and related stochastic differential games[J]. Frontiers of Mathematics in China, 2020 , 15(6) : 1307 -1326 . DOI: 10.1007/s11464-020-0889-y
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