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A Class of Solvable Stopping Games

Author

Listed:
  • Luis H. R. Alvarez E.

    (Department of Economics, Turku School of Economics)

Abstract

We consider a class of Dynkin games in the case where the underlying process evolves according to a one-dimensional but otherwise general diffusion. We establish general conditions under which both the value and the saddle point equilibrium exist and under which the exercise boundaries characterizing the saddle point strategy can be explicitly characterized in terms of a pair of standard first order necessary conditions for optimality. We also analyze those cases where an extremal pair of boundaries exists and show that there are circumstances under which increased volatility may break up the existence of a saddle point.

Suggested Citation

  • Luis H. R. Alvarez E., 2006. "A Class of Solvable Stopping Games," Discussion Papers 11, Aboa Centre for Economics.
    • Handle: RePEc:tkk:dpaper:dp11
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    File URL: http://www.ace-economics.fi/kuvat/ACE11%20Alvarez.pdf
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    References listed on IDEAS

    as
    1. Andreas Kyprianou, 2004. "Some calculations for Israeli options," Finance and Stochastics, Springer, vol. 8(1), pages 73-86, January.
    2. Erik Ekstrom & Stephane Villeneuve, 2006. "On the value of optimal stopping games," Papers math/0610324, arXiv.org.
    3. Luis H. R. Alvarez, 2001. "Reward functionals, salvage values, and optimal stopping," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 54(2), pages 315-337, December.
    4. Yuri Kifer, 2000. "Game options," Finance and Stochastics, Springer, vol. 4(4), pages 443-463.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Luis H. R. Alvarez E., 2006. "Minimum Guaranteed Payments and Costly Cancellation Rights: A Stopping Game Perspective," Discussion Papers 12, Aboa Centre for Economics.
    2. Soren Christensen, 2011. "Optimal decision under ambiguity for diffusion processes," Papers 1110.3897, arXiv.org, revised Oct 2012.
    3. Yuri Kifer, 2012. "Dynkin Games and Israeli Options," Papers 1209.1791, arXiv.org.
    4. Giorgio Ferrari & Tiziano Vargiolu, 2020. "On the singular control of exchange rates," Annals of Operations Research, Springer, vol. 292(2), pages 795-832, September.

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    More about this item

    Keywords

    Dynkin games; linear diffusions; fundamental solutions; minimal excessive functions;
    All these keywords.

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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