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A solution technique for Lévy driven long term average impulse control problems

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  • Christensen, Sören
  • Sohr, Tobias

Abstract

This article treats long term average impulse control problems with running costs in the case that the underlying process is a Lévy process. Assuming a maximum representation for the payoff function, we give easy to verify conditions for the control problem to have an s,S strategy as an optimizer. The occurring thresholds are given by the roots of an explicit auxiliary function. This leads to a step by step solution technique whose utility we demonstrate by solving a variety of examples of impulse control problems.

Suggested Citation

  • Christensen, Sören & Sohr, Tobias, 2020. "A solution technique for Lévy driven long term average impulse control problems," Stochastic Processes and their Applications, Elsevier, vol. 130(12), pages 7303-7337.
    • Handle: RePEc:eee:spapps:v:130:y:2020:i:12:p:7303-7337
    DOI: 10.1016/j.spa.2020.07.016
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    References listed on IDEAS

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    1. Shackleton, Mark B. & Sødal, Sigbjørn, 2010. "Harvesting and recovery decisions under uncertainty," Journal of Economic Dynamics and Control, Elsevier, vol. 34(12), pages 2533-2546, December.
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    3. Christensen, Sören, 2014. "On the solution of general impulse control problems using superharmonic functions," Stochastic Processes and their Applications, Elsevier, vol. 124(1), pages 709-729.
    4. Mundaca, Gabriela & Oksendal, Bernt, 1998. "Optimal stochastic intervention control with application to the exchange rate," Journal of Mathematical Economics, Elsevier, vol. 29(2), pages 225-243, March.
    5. Ralf Korn, 1999. "Some applications of impulse control in mathematical finance," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 50(3), pages 493-518, December.
    6. Willassen, Yngve, 1998. "The stochastic rotation problem: A generalization of Faustmann's formula to stochastic forest growth," Journal of Economic Dynamics and Control, Elsevier, vol. 22(4), pages 573-596, April.
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    Cited by:

    1. Soren Christensen & Albrecht Irle & Julian Peter Lemburg, 2021. "Flexible forward improvement iteration for infinite time horizon Markovian optimal stopping problems," Papers 2111.13443, arXiv.org.

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