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Deterministic minimax impulse control in finite horizon: the viscosity solution approach∗∗∗

Published online by Cambridge University Press:  22 March 2012

Brahim El Asri
Brahim El Asri*
Affiliation:
Institut für Stochastik, Friedrich-Schiller-Universität Jena, Ernst-Abbe-Platz 2, 07743 Jena, Germany. brahim.el-asri@uni-jena.de
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Abstract

We study here the impulse control minimax problem. We allow the cost functionals and dynamics to be unbounded and hence the value functions can possibly be unbounded. We prove that the value function of the problem is continuous. Moreover, the value function is characterized as the unique viscosity solution of an Isaacs quasi-variational inequality. This problem is in relation with an application in mathematical finance.

Keywords

Impulse controlrobust controldifferential gamesquasi-variational inequalityviscosity solution
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 19 , Issue 1 , January 2013 , pp. 63 - 77
Copyright
© EDP Sciences, SMAI, 2012

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