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Stochastic maximum principle for non-zero sum differential games of FBSDEs with impulse controls and its application to finance

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  • This paper is concerned with a maximum principle for a new class of non-zero sum stochastic differential games. Compared with the existing literature, the game systems in this paper are forward-backward systems in which the control variables consist of two components: the continuous controls and the impulse controls. Necessary optimality conditions and sufficient optimality conditions in the form of maximum principle are obtained respectively for open-loop Nash equilibrium point of the foregoing games. A fund management problem is used to shed light on the application of the theoretical results, and the optimal investment portfolio and optimal impulse consumption strategy are obtained explicitly.
    Mathematics Subject Classification: Primary: 93E20, 91A23; Secondary: 91G80.

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