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Flexible forward improvement iteration for infinite time horizon Markovian optimal stopping problems

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  • Soren Christensen
  • Albrecht Irle
  • Julian Peter Lemburg

Abstract

In this paper, we propose an extension of the forward improvement iteration algorithm, originally introduced in Irle (2006) and recently reconsidered in Miclo and Villeneuve (2021). The main new ingredient is a flexible window parameter describing the look-ahead distance in the improvement step. We consider the framework of a Markovian optimal stopping problem in discrete time with random discounting and infinite time horizon. We prove convergence and show that the additional flexibility may significantly reduce the runtime.

Suggested Citation

  • 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.
    • Handle: RePEc:arx:papers:2111.13443
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    References listed on IDEAS

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    1. Isaac Sonin, 1999. "The Elimination algorithm for the problem of optimal stopping," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 49(1), pages 111-123, March.
    2. Christensen, Sören & Irle, Albrecht, 2020. "The monotone case approach for the solution of certain multidimensional optimal stopping problems," Stochastic Processes and their Applications, Elsevier, vol. 130(4), pages 1972-1993.
    3. 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.
    4. Anastasia Kolodko & John Schoenmakers, 2006. "Iterative construction of the optimal Bermudan stopping time," Finance and Stochastics, Springer, vol. 10(1), pages 27-49, January.
    5. Sören Christensen, 2014. "A Method For Pricing American Options Using Semi-Infinite Linear Programming," Mathematical Finance, Wiley Blackwell, vol. 24(1), pages 156-172, January.
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