Deterministic minimax impulse control in finite horizon: the viscosity solution approach

Brahim El Asri

ESAIM: Control, Optimisation and Calculus of Variations (2013)

  • Volume: 19, Issue: 1, page 63-77
  • ISSN: 1292-8119

Abstract

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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.

How to cite

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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 19.1 (2013): 63-77. <http://eudml.org/doc/272769>.

@article{ElAsri2013,
abstract = {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.},
author = {El Asri, Brahim},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {impulse control; robust control; differential games; quasi-variational inequality; viscosity solution},
language = {eng},
number = {1},
pages = {63-77},
publisher = {EDP-Sciences},
title = {Deterministic minimax impulse control in finite horizon: the viscosity solution approach},
url = {http://eudml.org/doc/272769},
volume = {19},
year = {2013},
}

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
PB - EDP-Sciences
VL - 19
IS - 1
SP - 63
EP - 77
AB - 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.
LA - eng
KW - impulse control; robust control; differential games; quasi-variational inequality; viscosity solution
UR - http://eudml.org/doc/272769
ER -

References

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