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 control, robust control, differential games, quasi-variational inequality, viscosity solution

@article{COCV_2013__19_1_63_0, author = {El Asri, Brahim}, 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}, volume = {19}, number = {1}, year = {2013}, doi = {10.1051/cocv/2011200}, mrnumber = {3023060}, zbl = {1259.49011}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/cocv/2011200/} }

TY - JOUR AU - El Asri, Brahim TI - Deterministic minimax impulse control in finite horizon: the viscosity solution approach JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2013 SP - 63 EP - 77 VL - 19 IS - 1 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv/2011200/ DO - 10.1051/cocv/2011200 LA - en ID - COCV_2013__19_1_63_0 ER -

%0 Journal Article %A El Asri, Brahim %T Deterministic minimax impulse control in finite horizon: the viscosity solution approach %J ESAIM: Control, Optimisation and Calculus of Variations %D 2013 %P 63-77 %V 19 %N 1 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv/2011200/ %R 10.1051/cocv/2011200 %G en %F COCV_2013__19_1_63_0

El Asri, Brahim. Deterministic minimax impulse control in finite horizon: the viscosity solution approach. ESAIM: Control, Optimisation and Calculus of Variations, Volume 19 (2013) no. 1, pp. 63-77. doi : 10.1051/cocv/2011200. http://archive.numdam.org/articles/10.1051/cocv/2011200/

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