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

Dejian Chang; Zhen Wu

doi:10.3934/jimo.2015.11.27

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2015, Volume 11, Issue 1: 27-40. Doi: 10.3934/jimo.2015.11.27

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

Dejian Chang^1, and
Zhen Wu^1,

1.
School of Mathematics, Shandong University, Jinan 250100

Received: December 31, 2012

Revised: October 31, 2013

Published: December 2014

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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 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.

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Mathematics Subject Classification: Primary: 93E20, 91A23; Secondary: 91G80.

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