Backward linear quadratic stochastic optimal control problems and nonzero sum differential games

Abstract

In R. Buckdahn, Li, Peng [6], the authors obtained mean-field backward stochastic Differential equations (BSDEs) in a natural way as a limit of some highly dimensional system of forward and backward SDEs, corresponding to a great number of particles. In this paper, firstly, we prove that there exists a unique solution of fully coupled MF-FBSDE. Then we use the solutions of mean-field forward-backward stochastic differential equations to get the explicit form of the optimal control for linear quadratic optimal control problem and the open-loop Nash equilibrium point of nonzero sum differential games.