IDEAS home Printed from https://ideas.repec.org/a/inm/ormoor/v50y2025i3p1832-1867.html
   My bibliography  Save this article

Nonzero-Sum Optimal Stopping Game with Continuous vs. Periodic Exercise Opportunities

Author

Listed:
  • José Luis Pérez

    (Department of Probability and Statistics, Centro de Investigación en Matemáticas, 36240 Guanajuato, Mexico)

  • Neofytos Rodosthenous

    (Department of Mathematics, University College London, London WC1E 6BT, United Kingdom)

  • Kazutoshi Yamazaki

    (School of Mathematics and Physics, The University of Queensland, Brisbane, Queensland 4072, Australia)

Abstract

We introduce a new nonzero-sum game of optimal stopping with asymmetric exercise opportunities. Given a stochastic process modeling the value of an asset, one player observes and can act on the process continuously, whereas the other player can act on it only periodically at independent Poisson arrival times. The first one to stop receives a reward, different for each player, whereas the other one gets nothing. We study how each player balances the maximization of gains against the maximization of the likelihood of stopping before the opponent. In such a setup driven by a Lévy process with positive jumps, we not only prove the existence but also explicitly construct a Nash equilibrium with values of the game written in terms of the scale function. Numerical illustrations with put-option payoffs are also provided to study the behavior of the players’ strategies as well as the quantification of the value of available exercise opportunities.

Suggested Citation

  • José Luis Pérez & Neofytos Rodosthenous & Kazutoshi Yamazaki, 2025. "Nonzero-Sum Optimal Stopping Game with Continuous vs. Periodic Exercise Opportunities," Mathematics of Operations Research, INFORMS, vol. 50(3), pages 1832-1867, August.
    • Handle: RePEc:inm:ormoor:v:50:y:2025:i:3:p:1832-1867
    DOI: 10.1287/moor.2023.0123
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/moor.2023.0123
    Download Restriction: no
    File URL: https://libkey.io/10.1287/moor.2023.0123?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    More about this item

    Keywords

    ;
    ;
    ;
    ;

    JEL classification:

    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:inm:ormoor:v:50:y:2025:i:3:p:1832-1867. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.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.