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Optimal Stochastic Impulse Control with Delayed Reaction

Optimal Stochastic Impulse Control with Delayed Reaction We study impulse control problems of jump diffusions with delayed reaction. This means that there is a delay δ >0 between the time when a decision for intervention is taken and the time when the intervention is actually carried out. We show that under certain conditions this problem can be transformed into a sequence of iterated no-delay optimal stopping problems and there is an explicit relation between the solutions of these two problems. The results are illustrated by an example where the problem is to find the optimal times to increase the production capacity of a firm, assuming that there are transaction costs with each new order and the increase takes place δ time units after the (irreversible) order has been placed. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

Optimal Stochastic Impulse Control with Delayed Reaction

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Publisher
Springer Journals
Copyright
Copyright © 2008 by Springer Science+Business Media, LLC
Subject
Mathematics; Numerical and Computational Methods ; Mathematical Methods in Physics; Mathematical and Computational Physics; Systems Theory, Control; Calculus of Variations and Optimal Control; Optimization
ISSN
0095-4616
eISSN
1432-0606
DOI
10.1007/s00245-007-9034-5
Publisher site
See Article on Publisher Site

Abstract

We study impulse control problems of jump diffusions with delayed reaction. This means that there is a delay δ >0 between the time when a decision for intervention is taken and the time when the intervention is actually carried out. We show that under certain conditions this problem can be transformed into a sequence of iterated no-delay optimal stopping problems and there is an explicit relation between the solutions of these two problems. The results are illustrated by an example where the problem is to find the optimal times to increase the production capacity of a firm, assuming that there are transaction costs with each new order and the increase takes place δ time units after the (irreversible) order has been placed.

Journal

Applied Mathematics and OptimizationSpringer Journals

Published: Oct 1, 2008

References