Deterministic minimax impulse control in finite horizon: the viscosity solution approach
ESAIM: Control, Optimisation and Calculus of Variations, Tome 19 (2013) no. 1, pp. 63-77.

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.

DOI : 10.1051/cocv/2011200
Classification : 34H05, 34K35, 49L20, 49L25
Mots-clés : impulse control, robust control, differential games, quasi-variational inequality, viscosity solution 
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     title = {Deterministic minimax impulse control in finite horizon: the viscosity solution approach},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {63--77},
     publisher = {EDP-Sciences},
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El Asri, Brahim. Deterministic minimax impulse control in finite horizon: the viscosity solution approach. ESAIM: Control, Optimisation and Calculus of Variations, Tome 19 (2013) no. 1, pp. 63-77. doi : 10.1051/cocv/2011200. http://www.numdam.org/articles/10.1051/cocv/2011200/

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