IDEAS home Printed from https://ideas.repec.org/p/bie/wpaper/733.html
   My bibliography  Save this paper

Numerical approximation of Dynkin games with asymmetric information

Author

Listed:
  • Banas, Lubomir

    (Center for Mathematical Economics, Bielefeld University)

  • Ferrari, Giorgio

    (Center for Mathematical Economics, Bielefeld University)

  • Randrianasolo, Tsiry Avisoa

    (Center for Mathematical Economics, Bielefeld University)

Abstract

We propose an implementable, neural network-based structure preserving probabilistic numerical approximation for a generalized obstacle problem describing the value of a zero-sum differential game of optimal stopping with asymmetric information. The target solution depends on three variables: the time, the spatial (or state) variable, and a variable from a standard (I - 1)-simplex which represents the probabilities with which the I possible configurations of the game are played. The proposed numerical approximation preserves the convexity of the continuous solution as well as the lower and upper obstacle bounds. We show convergence of the fully-discrete scheme to the unique viscosity solution of the continuous problem and present a range of numerical studies to demonstrate its applicability.

Suggested Citation

  • Banas, Lubomir & Ferrari, Giorgio & Randrianasolo, Tsiry Avisoa, 2025. "Numerical approximation of Dynkin games with asymmetric information," Center for Mathematical Economics Working Papers 733, Center for Mathematical Economics, Bielefeld University.
    • Handle: RePEc:bie:wpaper:733
    as

    Download full text from publisher

    File URL: https://pub.uni-bielefeld.de/download/3006158/3006159
    File Function: First Version, 2024
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Fabien Gensbittel & Christine Grün, 2019. "Zero-Sum Stopping Games with Asymmetric Information," Mathematics of Operations Research, INFORMS, vol. 44(1), pages 277-302, February.
    2. Tiziano De Angelis & Erik Ekström & Kristoffer Glover, 2022. "Dynkin Games with Incomplete and Asymmetric Information," Mathematics of Operations Research, INFORMS, vol. 47(1), pages 560-586, February.
    3. Andreas Kyprianou, 2004. "Some calculations for Israeli options," Finance and Stochastics, Springer, vol. 8(1), pages 73-86, January.
    4. Christoph Kühn & Andreas E. Kyprianou, 2007. "Callable Puts As Composite Exotic Options," Mathematical Finance, Wiley Blackwell, vol. 17(4), pages 487-502, October.
    Full references (including those not matched with items on IDEAS)

    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. Tiziano De Angelis & Nikita Merkulov & Jan Palczewski, 2020. "On the value of non-Markovian Dynkin games with partial and asymmetric information," Papers 2007.10643, arXiv.org, revised Feb 2021.
    2. Guo, Peidong & Zhang, Jizhou & Wang, Qian, 2020. "Path-dependent game options with Asian features," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    3. Benjamin Gottesman Berdah, 2020. "Recombining tree approximations for Game Options in Local Volatility models," Papers 2007.02323, arXiv.org, revised Jul 2020.
    4. Hsuan-Ku Liu, 2013. "The pricing formula for cancellable European options," Papers 1304.5962, arXiv.org, revised Sep 2014.
    5. Hsuan-Ku Liu, 2021. "Perpetual callable American volatility options in a mean-reverting volatility model," Papers 2104.01127, arXiv.org.
    6. Tiziano De Angelis & Erik Ekstrom, 2019. "Playing with ghosts in a Dynkin game," Papers 1905.06564, arXiv.org.
    7. Tsvetelin S. Zaevski, 2022. "Pricing cancellable American put options on the finite time horizon," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 42(7), pages 1284-1303, July.
    8. Zaevski, Tsvetelin S., 2020. "Discounted perpetual game call options," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    9. Jacobovic, Royi & Levy, Yehuda John & Solan, Eilon, 0. "Bayesian games with nested information," Theoretical Economics, Econometric Society.
    10. H. Dharma Kwon & Jan Palczewski, 2022. "Exit game with private information," Papers 2210.01610, arXiv.org, revised Oct 2023.
    11. Huang, Haishi, 2010. "Convertible Bonds: Risks and Optimal Strategies," Bonn Econ Discussion Papers 07/2010, University of Bonn, Bonn Graduate School of Economics (BGSE).
    12. Peidong Guo & Qihong Chen & Xicai Guo & Yue Fang, 2014. "Path-dependent game options: a lookback case," Review of Derivatives Research, Springer, vol. 17(1), pages 113-124, April.
    13. David Hobson & Gechun Liang & Edward Wang, 2021. "Callable convertible bonds under liquidity constraints and hybrid priorities," Papers 2111.02554, arXiv.org, revised Oct 2024.
    14. Hertrich Markus, 2016. "The Costs of Implementing a Unilateral One-Sided Exchange Rate Target Zone," Review of Economics, De Gruyter, vol. 67(1), pages 91-120, May.
    15. Luis H. R. Alvarez E., 2006. "Minimum Guaranteed Payments and Costly Cancellation Rights: A Stopping Game Perspective," Discussion Papers 12, Aboa Centre for Economics.
    16. Boyarchenko, Svetlana & Levendorskiĭ, Sergei, 2014. "Preemption games under Lévy uncertainty," Games and Economic Behavior, Elsevier, vol. 88(C), pages 354-380.
    17. Tiziano De Angelis & Erik Ekström & Kristoffer Glover, 2022. "Dynkin Games with Incomplete and Asymmetric Information," Mathematics of Operations Research, INFORMS, vol. 47(1), pages 560-586, February.
    18. Starkov, Egor, 2023. "Only time will tell: Credible dynamic signaling," Journal of Mathematical Economics, Elsevier, vol. 109(C).
    19. Gunter H Meyer, 2016. "A PDE View of Games Options," Research Paper Series 369, Quantitative Finance Research Centre, University of Technology, Sydney.
    20. Yagi, Kyoko & Sawaki, Katsushige, 2010. "The pricing and optimal strategies of callable warrants," European Journal of Operational Research, Elsevier, vol. 206(1), pages 123-130, October.

    More about this item

    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:bie:wpaper:733. 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: Bettina Weingarten (email available below). General contact details of provider: https://edirc.repec.org/data/imbiede.html .

    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.