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In this article, we concern a kind of partially observed non-zero sumstochastic differential game based on forward and backward stochasticdifferential equations (FBSDEs). It is required that each player has his ownobservation equation, and the corresponding open-loop Nash equilibrium controlis required to adapted to the filtration that the observation processgenerated. To find this open-loop Nash equilibrium point, we prove the maximumprinciple as a necessary condition of the existence of this point, and give averification theorem as a sufficient condition to verify it is the realopen-loop Nash equilibrium point. Combined this with reality, a financialinvestment problem is raised. We can obtain the explicit observable investmentstrategy by using stochastic filtering theory and the results above.

A partially observed non-zero sum differential game of forward-backward stochastic differential equations and its application in finance