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Impulse control and expected suprema

Published online by Cambridge University Press:  17 March 2017

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: soeren.christensen@uni-hamburg.de
** Postal address: Department of Mathematics and Statistics, Åbo Akademi University, FIN-20500 Åbo, Finland.

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.

Type
Research Article
Copyright
Copyright © Applied Probability Trust 2017 

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