Abstract
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 gamesystems 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 equilibriumpoint of the foregoing games. A fund management problem is used to shed light on the application of the theoretical results, and the optimal investmentportfolio and optimal impulse consumption strategy are obtained explicitly.
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