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Linear - quadratic optimal control and nonzero-sum differential game of forward-backward stochastic system. (English) Zbl 1282.93280

Summary: An existence and uniqueness result for one kind of forward-backward stochastic differential equations with double dimensions was obtained under some monotonicity conditions. Then this result was applied to the linear-quadratic stochastic optimal control and nonzero-sum differential game of forward-backward stochastic system. The explicit forms of the optimal control and the Nash equilibrium point are obtained respectively. We note that our method is effective in studying the uniqueness of Nash equilibrium point.

MSC:

93E20 Optimal stochastic control
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
49N10 Linear-quadratic optimal control problems
49N70 Differential games and control
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