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On the value of optimal stopping games

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Author Info

  • Erik Ekstr\"{o}m
  • 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.

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File URL: http://arxiv.org/pdf/math/0610324
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Bibliographic Info

Paper provided by arXiv.org in its series Papers with number math/0610324.

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Date of creation: Oct 2006
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Publication status: Published in Annals of Applied Probability 2006, Vol. 16, No. 3, 1576-1596
Handle: RePEc:arx:papers:math/0610324

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Web page: http://arxiv.org/

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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. Yuri Kifer, 2012. "Dynkin Games and Israeli Options," Papers 1209.1791, arXiv.org.
  2. S\"oren Christensen, 2011. "Optimal decision under ambiguity for diffusion processes," Papers 1110.3897, arXiv.org, revised Oct 2012.
  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. Yan Dolinsky, 2011. "Hedging of Game Options With the Presence of Transaction Costs," Papers 1103.1165, arXiv.org, revised Mar 2012.
  5. Sören Christensen, 2013. "Optimal decision under ambiguity for diffusion processes," Computational Statistics, Springer, vol. 77(2), pages 207-226, April.

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