Maximum principle for mean-field zero-sum stochastic differential game with partial information and its application to finance

In this paper, we investigate the stochastic optimal control problem for the zero-sum stochastic differential game of mean-field type with partial information. We derive a necessary and sufficient maximum principle for that problem by virtue of the duality method and the mean-field backward stochastic differential equations. As an application, we apply the result to the mean-field stochastic differential portfolio game problem, and obtain an equilibrium point of such game.