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Optimal multiple stopping with random waiting times

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  • Soren Christensen
  • Albrecht Irle
  • Stephan Jurgens

Abstract

In the standard models for optimal multiple stopping problems it is assumed that between two exercises there is always a time period of deterministic length $\delta$, the so called refraction period. This prevents the optimal exercise times from bunching up together on top of the optimal stopping time for the one-exercise case. In this article we generalize the standard model by considering random refraction times. We develop the theory and reduce the problem to a sequence of ordinary stopping problems thus extending the results for deterministic times. This requires an extension of the underlying filtrations in general. Furthermore we consider the Markovian case and treat an example explicitly.

Suggested Citation

  • Soren Christensen & Albrecht Irle & Stephan Jurgens, 2012. "Optimal multiple stopping with random waiting times," Papers 1205.1966, arXiv.org.
  • Handle: RePEc:arx:papers:1205.1966
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    File URL: http://arxiv.org/pdf/1205.1966
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    References listed on IDEAS

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    1. Thompson, Andrew C., 1995. "Valuation of Path-Dependent Contingent Claims with Multiple Exercise Decisions over Time: The Case of Take-or-Pay," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 30(02), pages 271-293, June.
    2. Christian Bender, 2011. "Dual pricing of multi-exercise options under volume constraints," Finance and Stochastics, Springer, vol. 15(1), pages 1-26, January.
    3. René Carmona & Nizar Touzi, 2008. "Optimal Multiple Stopping And Valuation Of Swing Options," Mathematical Finance, Wiley Blackwell, vol. 18(2), pages 239-268.
    4. Patrick Jaillet & Ehud I. Ronn & Stathis Tompaidis, 2004. "Valuation of Commodity-Based Swing Options," Management Science, INFORMS, vol. 50(7), pages 909-921, July.
    5. N. Meinshausen & B. M. Hambly, 2004. "Monte Carlo Methods For The Valuation Of Multiple-Exercise Options," Mathematical Finance, Wiley Blackwell, vol. 14(4), pages 557-583.
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