The value of a minimax problem involving impulse control

Brahim El Asri

doi:10.3934/jdg.2019001

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2019, Volume 6, Issue 1: 1-17. Doi: 10.3934/jdg.2019001

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The value of a minimax problem involving impulse control

Brahim El Asri

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

Received: January 31, 2018

Revised: November 30, 2018

Published: December 2018

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Abstract

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.

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Mathematics Subject Classification: Primary: 49N25, 91G80, 49N70; Secondary: 35R45, 49L25.

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