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An optimal stopping problem in a diffusion-type model with delay

Author

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  • Pavel V. Gapeev
  • Markus Reiß

Abstract

We present an explicit solution to an optimal stopping problem in a model described by a stochastic delay differential equation with an exponential delay measure. The method of proof is based on reducing the initial problem to a free-boundary problem and solving the latter by means of the smooth-fit condition. The problem can be interpreted as pricing special perpetual average American put options in a diffusion-type model with delay.

Suggested Citation

  • Pavel V. Gapeev & Markus Reiß, 2005. "An optimal stopping problem in a diffusion-type model with delay," SFB 649 Discussion Papers SFB649DP2005-005, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    • Handle: RePEc:hum:wpaper:sfb649dp2005-005
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    File URL: http://sfb649.wiwi.hu-berlin.de/papers/pdf/SFB649DP2005-005.pdf
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    Cited by:

    1. Gapeev, Pavel V., 2020. "Optimal stopping problems for running minima with positive discounting rates," LSE Research Online Documents on Economics 105849, London School of Economics and Political Science, LSE Library.
    2. Marie Bernhart & Peter Tankov & Xavier Warin, 2010. "A finite dimensional approximation for pricing moving average options," Working Papers hal-00554216, HAL.
    3. Gapeev, Pavel V., 2008. "The integral option in a model with jumps," Statistics & Probability Letters, Elsevier, vol. 78(16), pages 2623-2631, November.
    4. Gapeev, Pavel V., 2020. "Optimal stopping problems for running minima with positive discounting rates," Statistics & Probability Letters, Elsevier, vol. 167(C).

    More about this item

    Keywords

    Optimal stopping; stochastic delay differential equation; diffusion process; sufficient statistic; free-boundary problem; smooth fit; Girsanov’s theorem; Ito’s formula;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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