A zero-sum stochastic differential game problem on infinite horizon with continuous and impulse controls is studied. We obtain the existence of the value of the game and characterize it as the unique viscosity solution of the associated system of quasi-variational inequalities. We also obtain a verification theorem which provides an optimal strategy of the game.
Mots clés : stochastic differential game, impulse control, quasi-variational inequalities, viscosity solution
@article{COCV_2011__17_3_749_0,
author = {Zhang, Feng},
title = {Stochastic differential games involving impulse controls},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {749--760},
publisher = {EDP-Sciences},
volume = {17},
number = {3},
year = {2011},
doi = {10.1051/cocv/2010023},
mrnumber = {2826978},
zbl = {1223.93121},
language = {en},
url = {http://www.numdam.org/articles/10.1051/cocv/2010023/}
}
TY - JOUR AU - Zhang, Feng TI - Stochastic differential games involving impulse controls JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2011 SP - 749 EP - 760 VL - 17 IS - 3 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv/2010023/ DO - 10.1051/cocv/2010023 LA - en ID - COCV_2011__17_3_749_0 ER -
%0 Journal Article %A Zhang, Feng %T Stochastic differential games involving impulse controls %J ESAIM: Control, Optimisation and Calculus of Variations %D 2011 %P 749-760 %V 17 %N 3 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv/2010023/ %R 10.1051/cocv/2010023 %G en %F COCV_2011__17_3_749_0
Zhang, Feng. Stochastic differential games involving impulse controls. ESAIM: Control, Optimisation and Calculus of Variations, Tome 17 (2011) no. 3, pp. 749-760. doi : 10.1051/cocv/2010023. http://www.numdam.org/articles/10.1051/cocv/2010023/
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