# American Institute of Mathematical Sciences

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doi: 10.3934/mcrf.2020022

## Stochastic impulse control Problem with state and time dependent cost functions

 1 Equipe. Aide à la decision, Université Ibn Zohr, ENSA, B.P. 1136, Agadir, Maroc 2 Department of Mathematical Sciences, Norwegian University of Sciences and Technology, Trondheim, 7491 Norway

Received  August 2019 Revised  November 2019 Published  March 2020

We consider stochastic impulse control problems when the impulses cost functions depend on $t$ and $x$. We use the approximation scheme and viscosity solutions approach to show that the value function is a unique viscosity solution for the associated Hamilton-Jacobi-Bellman equation (HJB) partial differential equation (PDE) of stochastic impulse control problems.

Citation: Brahim El Asri, Sehail Mazid. Stochastic impulse control Problem with state and time dependent cost functions. Mathematical Control & Related Fields, doi: 10.3934/mcrf.2020022
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