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On the value of optimal stopping games

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  • Erik Ekstrom
  • Stephane Villeneuve

Abstract

We show, under weaker assumptions than in the previous literature, that a perpetual optimal stopping game always has a value. We also show that there exists an optimal stopping time for the seller, but not necessarily for the buyer. Moreover, conditions are provided under which the existence of an optimal stopping time for the buyer is guaranteed. The results are illustrated explicitly in two examples.

Suggested Citation

  • Erik Ekstrom & Stephane Villeneuve, 2006. "On the value of optimal stopping games," Papers math/0610324, arXiv.org.
    • Handle: RePEc:arx:papers:math/0610324
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    References listed on IDEAS

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    1. Bergman, Yaacov Z & Grundy, Bruce D & Wiener, Zvi, 1996. "General Properties of Option Prices," Journal of Finance, American Finance Association, vol. 51(5), pages 1573-1610, December.
    2. Nicole El Karoui & Monique Jeanblanc‐Picquè & Steven E. Shreve, 1998. "Robustness of the Black and Scholes Formula," Mathematical Finance, Wiley Blackwell, vol. 8(2), pages 93-126, April.
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    Cited by:

    1. Tiziano De Angelis & Fabien Gensbittel & St'ephane Villeneuve, 2017. "A Dynkin game on assets with incomplete information on the return," Papers 1705.07352, arXiv.org, revised May 2019.
    2. Sandroni, Alvaro & Urgun, Can, 2017. "Dynamics in Art of War," Mathematical Social Sciences, Elsevier, vol. 86(C), pages 51-58.
    3. Boyarchenko, Svetlana & Levendorskiĭ, Sergei, 2014. "Preemption games under Lévy uncertainty," Games and Economic Behavior, Elsevier, vol. 88(C), pages 354-380.
    4. Luis H. R. Alvarez E., 2006. "A Class of Solvable Stopping Games," Discussion Papers 11, Aboa Centre for Economics.
    5. Tiziano De Angelis, 2020. "Stopping spikes, continuation bays and other features of optimal stopping with finite-time horizon," Papers 2009.01276, arXiv.org, revised Jan 2022.
    6. 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.
    7. Luis H. R. Alvarez E. & Paavo Salminen, 2017. "Timing in the presence of directional predictability: optimal stopping of skew Brownian motion," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 86(2), pages 377-400, October.
    8. Sören Christensen, 2013. "Optimal decision under ambiguity for diffusion processes," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 77(2), pages 207-226, April.
    9. Yan Dolinsky & Ariel Neufeld, 2015. "Super-replication in Fully Incomplete Markets," Papers 1508.05233, arXiv.org, revised Sep 2016.
    10. Yan Dolinsky, 2011. "Hedging of Game Options With the Presence of Transaction Costs," Papers 1103.1165, arXiv.org, revised Mar 2012.
    11. Aradhye, Aditya & Flesch, János & Staudigl, Mathias & Vermeulen, Dries, 2023. "Incentive compatibility in sender-receiver stopping games," Games and Economic Behavior, Elsevier, vol. 141(C), pages 303-320.
    12. Wong, Tat Wing & Fung, Ka Wai Terence & Leung, Kwai Sun, 2020. "Strategic bank closure and deposit insurance valuation," European Journal of Operational Research, Elsevier, vol. 285(1), pages 96-105.
    13. Zaevski, Tsvetelin S., 2020. "Discounted perpetual game call options," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    14. Luis H. R. Alvarez E., 2006. "Minimum Guaranteed Payments and Costly Cancellation Rights: A Stopping Game Perspective," Discussion Papers 12, Aboa Centre for Economics.
    15. Said Hamadene & Jianfeng Zhang, 2008. "The Continuous Time Nonzero-sum Dynkin Game Problem and Application in Game Options," Papers 0810.5698, arXiv.org.
    16. Soren Christensen, 2011. "Optimal decision under ambiguity for diffusion processes," Papers 1110.3897, arXiv.org, revised Oct 2012.
    17. Yuri Kifer, 2012. "Dynkin Games and Israeli Options," Papers 1209.1791, arXiv.org.
    18. Tiziano De Angelis & Fabien Gensbittel & Stephane Villeneuve, 2021. "A Dynkin Game on Assets with Incomplete Information on the Return," Mathematics of Operations Research, INFORMS, vol. 46(1), pages 28-60, February.

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