Applied Mathematics & Optimization

, Volume 71, Issue 1, pp 95–123 | Cite as

Resolvent-Techniques for Multiple Exercise Problems

  • Sören Christensen
  • Jukka LempaEmail author


We study optimal multiple stopping of strong Markov processes with random refraction periods. The refraction periods are assumed to be exponentially distributed with a common rate and independent of the underlying dynamics. Our main tool is using the resolvent operator. In the first part, we reduce infinite stopping problems to ordinary ones in a general strong Markov setting. This leads to explicit solutions for wide classes of such problems. Starting from this result, we analyze problems with finitely many exercise rights and explain solution methods for some classes of problems with underlying Lévy and diffusion processes, where the optimal characteristics of the problems can be identified more explicitly. We illustrate the main results with explicit examples.


Optimal multiple stopping Stochastic impulse control Strong Markov process Lévy process Diffusion process Resolvent operator 

Mathematics Subject Classification

60J60 60G40 



We thank the anonymous referee for carefully reading earlier versions of this manuscript and for thoughtful and valuable comments that helped to improve the presentation of this article. Jukka Lempa acknowledges financial support from the project “Energy markets: modelling, optimization and simulation (EMMOS)”, funded by the Norwegian Research Council under Grant 205328.


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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Mathematical InstituteChristian–Albrechts-University in KielKielGermany
  2. 2.Department of Mathematics, SPSTUniversity of HamburgHamburgGermany
  3. 3.School of business, Faculty of Social SciencesOslo and Akershus University CollegeOsloNorway

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