# American Institute of Mathematical Sciences

January  2019, 6(1): 1-17. doi: 10.3934/jdg.2019001

## The value of a minimax problem involving impulse control

 Université Ibn Zohr, Equipe. Aide à la decision, ENSA, B.P. 1136, Agadir, Maroc

Received  February 2018 Revised  December 2018 Published  January 2019

We consider the minimax impulse control problem in finite horizon, when the cost functions are positive and not bounded from below with a strictly positive constant. We show existence of value function of the problem. Moreover, the value function is characterized as the unique viscosity solution of Hamilton-Jacobi-Bellman-Isaacs equation. This problem is in relation with an application in mathematical finance.

Citation: Brahim El Asri. The value of a minimax problem involving impulse control. Journal of Dynamics & Games, 2019, 6 (1) : 1-17. doi: 10.3934/jdg.2019001
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