| Issue |
ESAIM: COCV
Volume 19, Number 1, January-March 2013
|
|
|---|---|---|
| Page(s) | 63 - 77 | |
| DOI | https://doi.org/10.1051/cocv/2011200 | |
| Published online | 22 March 2012 | |
Deterministic minimax impulse control in finite horizon: the viscosity solution approach∗,∗∗
Institut für Stochastik, Friedrich-Schiller-Universität
Jena, Ernst-Abbe-Platz
2, 07743
Jena,
Germany
brahim.el-asri@uni-jena.de
Received:
13
July
2010
Revised:
13
October
2010
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.
Mathematics Subject Classification: 34H05 / 34K35 / 49L20 / 49L25
Key words: Impulse control / robust control / differential games / quasi-variational inequality / viscosity solution
© EDP Sciences, SMAI, 2012
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