  In this article, we concern a kind of partially observed non-zero sum
stochastic differential game based on forward and backward stochastic
differential equations (FBSDEs). It is required that each player has his own
observation equation, and the corresponding open-loop Nash equilibrium control
is required to adapted to the filtration that the observation process
generated. To find this open-loop Nash equilibrium point, we prove the maximum
principle as a necessary condition of the existence of this point, and give a
verification theorem as a sufficient condition to verify it is the real
open-loop Nash equilibrium point. Combined this with reality, a financial
investment problem is raised. We can obtain the explicit observable investment
strategy by using stochastic filtering theory and the results above.
