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Impulse control and expected suprema

Part of: Stochastic processes Miscellaneous topics in calculus of variations and optimal control

Published online by Cambridge University Press:  17 March 2017

Sören Christensen  and
Paavo Salminen
Sören Christensen*
Affiliation:
Chalmers University of Technology and University of Gothenburg
Paavo Salminen*
Affiliation:
Åbo Akademi University
*
* Current address: Department of Mathematics, University of Hamburg, Bundesstr. 55, 20146 Hamburg, Germany. Email address: [email protected]
** Postal address: Department of Mathematics and Statistics, Åbo Akademi University, FIN-20500 Åbo, Finland.
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Abstract

We consider a class of impulse control problems for general underlying strong Markov processes on the real line, which allows for an explicit solution. The optimal impulse times are shown to be of a threshold type and the optimal threshold is characterised as a solution of a (typically nonlinear) equation. The main ingredient we use is a representation result for excessive functions in terms of expected suprema.

Keywords

Impulse controlHunt processthreshold ruleexcessive function

MSC classification

Primary: 49N25: Impulsive optimal control problems
Secondary: 60G40: Stopping times; optimal stopping problems; gambling theory
Type
Research Article
Information
Advances in Applied Probability , Volume 49 , Issue 1 , March 2017 , pp. 238 - 257
Copyright
Copyright © Applied Probability Trust 2017 

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