IDEAS home Printed from https://ideas.repec.org/p/hal/wpaper/hal-00642919.html
   My bibliography  Save this paper

Optimal multiple stopping problem and financial applications

Author

Listed:
  • 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 - Ecole Polytechnique - X - École polytechnique - 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 - Ecole Polytechnique - X - École polytechnique - 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
    as

    Download full text from publisher

    File URL: https://inria.hal.science/hal-00642919/document
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Long, Mingsi & Zhang, Hongzhong, 2019. "On the optimality of threshold type strategies in single and recursive optimal stopping under Lévy models," Stochastic Processes and their Applications, Elsevier, vol. 129(8), pages 2821-2849.
    2. J. Lars Kirkby & Shi-Jie Deng, 2019. "Swing Option Pricing By Dynamic Programming With B-Spline Density Projection," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(08), pages 1-53, December.
    3. Marzia De Donno & Zbigniew Palmowski & Joanna Tumilewicz, 2020. "Double continuation regions for American and Swing options with negative discount rate in Lévy models," Mathematical Finance, Wiley Blackwell, vol. 30(1), pages 196-227, January.
    4. Tim Leung & Kazutoshi Yamazaki & Hongzhong Zhang, 2015. "Optimal Multiple Stopping with Negative Discount Rate and Random Refraction Times under Levy Models," Papers 1505.07313, arXiv.org.
    5. Mingsi Long & Hongzhong Zhang, 2017. "On the optimality of threshold type strategies in single and recursive optimal stopping under L\'evy models," Papers 1707.07797, arXiv.org, revised Aug 2018.
    6. Tim Leung & Kazutoshi Yamazaki & Hongzhong Zhang, 2015. "An Analytic Recursive Method For Optimal Multiple Stopping: Canadization And Phase-Type Fitting," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 18(05), pages 1-31.
    7. Christian Bender & Nikolai Dokuchaev, 2013. "A First-Order BSPDE for Swing Option Pricing," Papers 1305.3988, arXiv.org.
    8. S. C. P. Yam & W. Zhou, 2017. "Optimal Liquidation of Child Limit Orders," Mathematics of Operations Research, INFORMS, vol. 42(2), pages 517-545, May.
    9. Pavel V. Gapeev & Peter M. Kort & Maria N. Lavrutich & Jacco J. J. Thijssen, 2022. "Optimal Double Stopping Problems for Maxima and Minima of Geometric Brownian Motions," Methodology and Computing in Applied Probability, Springer, vol. 24(2), pages 789-813, June.
    10. Belleh Fontem, 2022. "An optimal stopping policy for car rental businesses with purchasing customers," Annals of Operations Research, Springer, vol. 317(1), pages 47-76, October.
    11. Rodrigo S. Targino & Gareth W. Peters & Georgy Sofronov & Pavel V. Shevchenko, 2017. "Optimal Exercise Strategies for Operational Risk Insurance via Multiple Stopping Times," Methodology and Computing in Applied Probability, Springer, vol. 19(2), pages 487-518, June.
    12. Pavel V. Gapeev, 2022. "Perpetual American Double Lookback Options on Drawdowns and Drawups with Floating Strikes," Methodology and Computing in Applied Probability, Springer, vol. 24(2), pages 749-788, June.
    13. Mr. Nikolay Aleksandrov & Mr. lajos Gyurko & Mr. Raphael A Espinoza, 2012. "Optimal Oil Production and the World Supply of Oil," IMF Working Papers 2012/294, International Monetary Fund.
    14. Rodrigo S. Targino & Gareth W. Peters & Georgy Sofronov & Pavel V. Shevchenko, 2013. "Optimal insurance purchase strategies via optimal multiple stopping times," Papers 1312.0424, arXiv.org.
    15. Jelito, Damian & Pitera, Marcin & Stettner, Łukasz, 2021. "Risk sensitive optimal stopping," Stochastic Processes and their Applications, Elsevier, vol. 136(C), pages 125-144.
    16. M’hamed Gaïgi & Stéphane Goutte & Idris Kharroubi & Thomas Lim, 2021. "Optimal risk management problem of natural resources: application to oil drilling," Annals of Operations Research, Springer, vol. 297(1), pages 147-166, February.
    17. Aleksandrov, Nikolay & Espinoza, Raphael & Gyurkó, Lajos, 2013. "Optimal oil production and the world supply of oil," Journal of Economic Dynamics and Control, Elsevier, vol. 37(7), pages 1248-1263.
    18. Christian Yeo, 2023. "An analysis of least squares regression and neural networks approximation for the pricing of swing options," Papers 2307.04510, arXiv.org.
    19. John Moriarty & Jan Palczewski, 2019. "Imbalance Market Real Options and the Valuation of Storage in Future Energy Systems," Risks, MDPI, vol. 7(2), pages 1-30, April.
    20. Dahlgren, Eric & Leung, Tim, 2015. "An optimal multiple stopping approach to infrastructure investment decisions," Journal of Economic Dynamics and Control, Elsevier, vol. 53(C), pages 251-267.

    More about this item

    Keywords

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

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:hal:wpaper:hal-00642919. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: CCSD (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.