Stochastic differential games of fully coupled forward-backward stochastic systems under partial information

In this paper, an open-loop two-person zero-sum stochastic differential game is considered under partial information. More precisely, the controlled systems are described by a fully coupled nonlinear multi-dimensional forward-backward stochastic differential equation driven by a multi-dimensional Brownian motion, and all admissible control processes for both players are required to be adapted to a given subfiltration of the filtration generated by the underlying Brownian motion. For this type of partial information stochastic differential game, one sufficient (a verification theorem) and one necessary conditions for the existence of open-loop saddle points for the corresponding two-person zero-sum stochastic differential game are proved. The control domain need to be convex and the admissible controls for both players are allowed to appear in both the drift and diffusion of the state equations.