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Optimal multiple stopping problem and financial applications

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Author Info

  • Imene Ben Latifa

    (LAMSIN - Laboratoire de Modélisation Mathématique et Numérique dans les Sciences de l'Ingénieur - ENIT)

  • J. Frederic Bonnans

    ()
    (INRIA Saclay - Ile de France - Commands - INRIA - CNRS : UMR7641 - Polytechnique - X - ENSTA ParisTech, CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique - Polytechnique - X - CNRS : UMR7641)

  • Mohamed Mnif

    (LAMSIN - Laboratoire de Modélisation Mathématique et Numérique dans les Sciences de l'Ingénieur - ENIT)

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    Abstract

    In their paper [2], Carmona and Touzi have studied an optimal multiple stopping time problem in a market where the price process is continuous. In this paper, we generalize their results when the price process is allowed to jump. Also, we generalize the problem associated to the valuation of swing options to the context of jump diffusion processes. Then we relate our problem to a sequence of ordinary stopping time problems. We characterize the value function of each ordinary stopping time problem as the unique viscosity solution of the associated Hamilton-Jacobi-Bellman Variational Inequality.

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    File URL: http://hal.inria.fr/docs/00/64/29/19/PDF/RR-7807.pdf
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    Bibliographic Info

    Paper provided by HAL in its series Working Papers with number hal-00642919.

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    Date of creation: 19 Nov 2011
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    Handle: RePEc:hal:wpaper:hal-00642919

    Note: View the original document on HAL open archive server: http://hal.inria.fr/hal-00642919/en/
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    Web page: http://hal.archives-ouvertes.fr/

    Related research

    Keywords: Optimal multiple stopping ; swing option ; jump diffusion process ; Snell envelop ; viscosity solution.;

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    1. René Carmona & Nizar Touzi, 2008. "Optimal Multiple Stopping And Valuation Of Swing Options," Mathematical Finance, Wiley Blackwell, vol. 18(2), pages 239-268.
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