Maximum principle for non-zero sum differential games of BSDEs involving impulse controls

This paper is concerned with a new kind of non-zero sum stochastic differential games of backward differential equations involving impulse controls. The most distinguishing features of our problem are that the control variables consist of the regular part and the impulsive part and that the domain of regular control is not necessarily convex. We establish a necessary condition in the form of maximum principle with Pontryagin´s type for the open-loop Nash equilibrium point of this game, and then give a verification theorem which is a sufficient condition for Nash equilibrium point. The theoretical results are applied to study a linear-quadratic differential game and the equilibrium point is obtained explicitly.