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On the Value of Optimal Stopping Games

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  • Stéphane Villeneuve

    () (GREMAQ - Groupe de recherche en économie mathématique et quantitative - UT1 - Université Toulouse 1 Capitole - INRA - Institut National de la Recherche Agronomique - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique)

  • Erik Ekstrom

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.
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Suggested Citation

  • Stéphane Villeneuve & Erik Ekstrom, 2006. "On the Value of Optimal Stopping Games," Post-Print hal-00173182, HAL.
    • Handle: RePEc:hal:journl:hal-00173182
    Note: View the original document on HAL open archive server: https://hal.archives-ouvertes.fr/hal-00173182
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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.
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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 Sep 2018.
    2. Luis H. R. Alvarez E., 2006. "Minimum Guaranteed Payments and Costly Cancellation Rights: A Stopping Game Perspective," Discussion Papers 12, Aboa Centre for Economics.
    3. Said Hamadene & Jianfeng Zhang, 2008. "The Continuous Time Nonzero-sum Dynkin Game Problem and Application in Game Options," Papers 0810.5698, arXiv.org.
    4. Yuri Kifer, 2012. "Dynkin Games and Israeli Options," Papers 1209.1791, arXiv.org.
    5. Sandroni, Alvaro & Urgun, Can, 2017. "Dynamics in Art of War," Mathematical Social Sciences, Elsevier, vol. 86(C), pages 51-58.
    6. Yan Dolinsky & Ariel Neufeld, 2015. "Super-replication in Fully Incomplete Markets," Papers 1508.05233, arXiv.org, revised Sep 2016.
    7. Yan Dolinsky, 2011. "Hedging of Game Options With the Presence of Transaction Costs," Papers 1103.1165, arXiv.org, revised Mar 2012.
    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. Soren Christensen, 2011. "Optimal decision under ambiguity for diffusion processes," Papers 1110.3897, arXiv.org, revised Oct 2012.
    10. Boyarchenko, Svetlana & Levendorskiĭ, Sergei, 2014. "Preemption games under Lévy uncertainty," Games and Economic Behavior, Elsevier, vol. 88(C), pages 354-380.
    11. Luis H. R. Alvarez E., 2006. "A Class of Solvable Stopping Games," Discussion Papers 11, Aboa Centre for Economics.
    12. repec:spr:mathme:v:86:y:2017:i:2:d:10.1007_s00186-017-0602-4 is not listed on IDEAS
    13. repec:spr:compst:v:77:y:2013:i:2:p:207-226 is not listed on IDEAS
    14. Luis H. R. Alvarez E. & Paavo Salminen, 2016. "Timing in the Presence of Directional Predictability: Optimal Stopping of Skew Brownian Motion," Papers 1608.04537, arXiv.org.

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