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Discounted Optimal Stopping for Maxima of some Jump-Diffusion Processes

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  • Pavel V. Gapeev

Abstract

We present solutions to some discounted optimal stopping problems for the maximum process in a model driven by a Brownian motion and a compound Poisson process with exponential jumps. The method of proof is based on reducing the initial problems to integro-differential free-boundary problems where the normal reflection and smooth fit may break down and the latter then be replaced by the continuous fit. The results can be interpreted as pricing perpetual American lookback options with fixed and floating strikes in a jump-diffusion model.

Suggested Citation

  • Pavel V. Gapeev, 2006. "Discounted Optimal Stopping for Maxima of some Jump-Diffusion Processes," SFB 649 Discussion Papers SFB649DP2006-059, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  • Handle: RePEc:hum:wpaper:sfb649dp2006-059
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    File URL: http://sfb649.wiwi.hu-berlin.de/papers/pdf/SFB649DP2006-059.pdf
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    References listed on IDEAS

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    1. S. G. Kou & Hui Wang, 2004. "Option Pricing Under a Double Exponential Jump Diffusion Model," Management Science, INFORMS, vol. 50(9), pages 1178-1192, September.
    2. Gapeev Pavel V. & Kühn Christoph, 2005. "Perpetual convertible bonds in jump-diffusion models," Statistics & Risk Modeling, De Gruyter, vol. 23(1/2005), pages 15-31, January.
    3. Duistermaat, J.J. & Kyprianou, A.E. & van Schaik, K., 2005. "Finite expiry Russian options," Stochastic Processes and their Applications, Elsevier, vol. 115(4), pages 609-638, April.
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    Cited by:

    1. repec:wsi:ijtafx:v:18:y:2015:i:02:n:s0219024915500089 is not listed on IDEAS
    2. Yerkin Kitapbayev, 2015. "The British Lookback Option with Fixed Strike," Applied Mathematical Finance, Taylor & Francis Journals, vol. 22(3), pages 238-260, July.

    More about this item

    Keywords

    Discounted optimal stopping problem; Brownian motion; compound Poisson process; maximum process; integro-differential free-boundary problem; continuous and smooth fit; normal reflection; a change-of-variable formula with local time on surfaces; perpetual lookback American options;

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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