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January  2015, 11(1): 27-40. doi: 10.3934/jimo.2015.11.27

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

 1 School of Mathematics, Shandong University, Jinan 250100, China, China

Received  January 2013 Revised  November 2013 Published  May 2014

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.
Citation: Dejian Chang, Zhen Wu. Stochastic maximum principle for non-zero sum differential games of FBSDEs with impulse controls and its application to finance. Journal of Industrial & Management Optimization, 2015, 11 (1) : 27-40. doi: 10.3934/jimo.2015.11.27
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