A partial information non-zero sum differential game of backward stochastic differential equations with applications.

*(English)*Zbl 1260.93181Summary: 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) |

##### Keywords:

backward stochastic differential equation; maximum principle; open-loop Nash equilibrium point; non-zero sum stochastic differential game; filtering; portfolio choice
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\textit{G. Wang} and \textit{Z. Yu}, Automatica 48, No. 2, 342--352 (2012; Zbl 1260.93181)

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