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Optimal multiple stopping problem and financial applications

Author

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  • Imene Ben Latifa

    (LR-LAMSIN-ENIT - Laboratoire de Modélisation Mathématique et Numérique dans les Sciences de l'Ingénieur [Tunis] - ENIT - Ecole Nationale d'Ingénieurs de Tunis - UTM - Université de Tunis El Manar)

  • Joseph Frederic Bonnans

    (Commands - Control, Optimization, Models, Methods and Applications for Nonlinear Dynamical Systems - CMAP - Centre de Mathématiques Appliquées de l'Ecole polytechnique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique - Inria Saclay - Ile de France - Inria - Institut National de Recherche en Informatique et en Automatique, CMAP - Centre de Mathématiques Appliquées de l'Ecole polytechnique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique)

  • Mohamed Mnif

    (LR-LAMSIN-ENIT - Laboratoire de Modélisation Mathématique et Numérique dans les Sciences de l'Ingénieur [Tunis] - ENIT - Ecole Nationale d'Ingénieurs de Tunis - UTM - Université de Tunis El Manar)

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.

Suggested Citation

  • Imene Ben Latifa & Joseph Frederic Bonnans & Mohamed Mnif, 2011. "Optimal multiple stopping problem and financial applications," Working Papers hal-00642919, HAL.
    • Handle: RePEc:hal:wpaper:hal-00642919
    Note: View the original document on HAL open archive server: https://inria.hal.science/hal-00642919
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    References listed on IDEAS

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    1. Amina Bouzguenda Zeghal & Mohamed Mnif, 2006. "Optimal Multiple Stopping And Valuation Of Swing Options In Lévy Models," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 9(08), pages 1267-1297.
    2. René Carmona & Nizar Touzi, 2008. "Optimal Multiple Stopping And Valuation Of Swing Options," Mathematical Finance, Wiley Blackwell, vol. 18(2), pages 239-268, April.
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    Cited by:

    1. Tiziano De Angelis & Yerkin Kitapbayev, 2014. "On the optimal exercise boundaries of swing put options," Papers 1407.6860, arXiv.org, revised Jan 2017.
    2. Tiziano De Angelis & Yerkin Kitapbayev, 2018. "On the Optimal Exercise Boundaries of Swing Put Options," Mathematics of Operations Research, INFORMS, vol. 43(1), pages 252-274, February.

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    More about this item

    Keywords

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