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A partial information non-zero sum differential game of backward stochastic differential equations with applications. (English) Zbl 1260.93181
Summary: This paper is concerned with a new kind of non-zero sum differential game of Backward Stochastic Differential Equations (BSDEs). It is required that the control is adapted to a sub-filtration of the filtration generated by the underlying Brownian motion. We establish a necessary condition in the form of Pontryagin’s maximum principle 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 and a partial information financial problem.

MSC:
93E20 Optimal stochastic control
49K45 Optimality conditions for problems involving randomness
91A23 Differential games (aspects of game theory)
91A15 Stochastic games, stochastic differential games
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
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