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The Continuous Time Nonzero-sum Dynkin Game Problem and Application in Game Options

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  • Said Hamadene
  • Jianfeng Zhang

Abstract

In this paper we study the nonzero-sum Dynkin game in continuous time which is a two player non-cooperative game on stopping times. We show that it has a Nash equilibrium point for general stochastic processes. As an application, we consider the problem of pricing American game contingent claims by the utility maximization approach.

Suggested Citation

  • Said Hamadene & Jianfeng Zhang, 2008. "The Continuous Time Nonzero-sum Dynkin Game Problem and Application in Game Options," Papers 0810.5698, arXiv.org.
    • Handle: RePEc:arx:papers:0810.5698
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    References listed on IDEAS

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    1. Touzi, N. & Vieille, N., 1999. "Continuous-Time Dynkin Games with Mixed Strategies," Papiers d'Economie Mathématique et Applications 1999.112, Université Panthéon-Sorbonne (Paris 1).
    2. Yoshio Ohtsubo, 1987. "A Nonzero-Sum Extension of Dynkin's Stopping Problem," Mathematics of Operations Research, INFORMS, vol. 12(2), pages 277-296, May.
    3. Jan Kallsen & Christoph Kühn, 2004. "Pricing derivatives of American and game type in incomplete markets," Finance and Stochastics, Springer, vol. 8(2), pages 261-284, May.
    4. Kuhn, Christoph, 2004. "Game contingent claims in complete and incomplete markets," Journal of Mathematical Economics, Elsevier, vol. 40(8), pages 889-902, December.
    5. Erik Ekstrom & Stephane Villeneuve, 2006. "On the value of optimal stopping games," Papers math/0610324, arXiv.org.
    6. Stéphane Villeneuve & Erik Ekstrom, 2006. "On the Value of Optimal Stopping Games," Post-Print hal-00173182, HAL.
    7. Rida Laraki & Eilon Solan, 2002. "Stopping Games in Continuous Time," Discussion Papers 1354, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    8. Baurdoux, Erik J. & Kyprianou, Andreas E., 2004. "Further calculations for Israeli options," LSE Research Online Documents on Economics 23916, London School of Economics and Political Science, LSE Library.
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    Cited by:

    1. Thomas J. Emmerling, 2010. "Perpetual Cancellable American Call Option," Papers 1009.3556, arXiv.org.
    2. Giovanni Mottola, 2014. "Reflected Backward SDE approach to the price-hedge of defaultable claims with contingent switching CSA," Papers 1412.1325, arXiv.org, revised Feb 2015.
    3. Giovanni Mottola, 2014. "Generalized Dynkin game of switching type representation for defaultable claims in presence of contingent CSA," Papers 1410.0594, arXiv.org, revised Jan 2015.

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