An asymmetric information non-zero sum differential game of mean-field backward stochastic differential equation with applications

Abstract

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.

Keywords

• Mean-field backward stochastic differential equation
• Asymmetric information
• Nash equilibrium point
• Maximum principle
• Filter