Nonzero Sum Differential Game of Mean-Field BSDEs with Jumps under Partial Information

Abstract EN

This paper is concerned with a kind of nonzero sum differential game of mean-field backward stochastic differential equations with jump (MF-BSDEJ), in which the coefficient contains not only the state process but also its marginal distribution.

Moreover, the cost functional is also of mean-field type.

It is required that the control is adapted to a subfiltration of the filtration generated by the underlying Brownian motion and Poisson random measure.

We establish a necessary condition in the form of maximum principle with Pontryagin’s type for open-loop Nash equilibrium point of this type of partial information game and then give a verification theorem which is a sufficient condition for Nash equilibrium point.

The theoretical results are applied to study a partial information linear-quadratic (LQ) game.