Abstract
This paper is concerned with a kind of non-zero sum differential game driven by mean-field backward stochastic differential equation (MF-BSDE) with asymmetric information, whose novel feature is that both the state equation and the cost functional are of mean-field type. A necessary condition and a sufficient condition for Nash equilibrium point of the above problem are established. As applications, a mean-field linear-quadratic (MF-LQ) problem and a financial problem are studied.
Highlights
Mean-field theory has been an active research field in recent years, which has attracted a lot of researchers to investigate this theory
We emphasize that the systems introduced in [3,4,5,6,7] are governed by forward stochastic differential equations (SDEs)
Wang and Yu [12] established a necessary condition and a verification theorem for open-loop Nash equilibrium point of non-zero sum differential game of BSDE under partial information
Summary
Mean-field theory has been an active research field in recent years, which has attracted a lot of researchers to investigate this theory. Hamadène and Lepeltier [11] discussed a stochastic zero-sum differential game of BSDE and obtained the existence of saddle point under the bounded case and Isaacs’ condition. Wang and Yu [12] established a necessary condition and a verification theorem for open-loop Nash equilibrium point of non-zero sum differential game of BSDE under partial information. Wang et al [13] discussed asymmetric information LQ non-zero sum differential game of BSDE and gave the feedback Nash equilibrium points. Wu and Liu [19] studied an optimal control problem for mean-field zero-sum stochastic differential game under partial information. We study a kind of asymmetric information non-zero sum differential game of MF-BSDE. We call the above problem a meanfield backward non-zero sum stochastic differential game with asymmetric information. If (u1(·), u2(·)) satisfies (3), we call it a Nash equilibrium point of Problem (MFBNZ)
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