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Solving finite time horizon Dynkin games by optimal switching

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  • Randall Martyr

Abstract

This paper uses recent results on continuous-time finite-horizon optimal switching problems with negative switching costs to prove the existence of a saddle point in an optimal stopping (Dynkin) game. Sufficient conditions for the game's value to be continuous with respect to the time horizon are obtained using recent results on norm estimates for doubly reflected backward stochastic differential equations. This theory is then demonstrated numerically for the special cases of cancellable call and put options in a Black-Scholes market.

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  • Randall Martyr, 2014. "Solving finite time horizon Dynkin games by optimal switching," Papers 1411.4438, arXiv.org, revised Jan 2016.
    • Handle: RePEc:arx:papers:1411.4438
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    References listed on IDEAS

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    1. Rene Carmona & Michael Ludkovski, 2008. "Pricing Asset Scheduling Flexibility using Optimal Switching," Applied Mathematical Finance, Taylor & Francis Journals, vol. 15(5-6), pages 405-447.
    2. de Angelis, Tiziano & Ferrari, Giorgio, 2014. "A Stochastic Reversible Investment Problem on a Finite-Time Horizon: Free Boundary Analysis," Center for Mathematical Economics Working Papers 477, Center for Mathematical Economics, Bielefeld University.
    3. Alexander Yushkevich & Evgueni Gordienko, 2002. "Average optimal switching of a Markov chain with a Borel state space," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 55(1), pages 143-159, March.
    4. Said Hamadène & Monique Jeanblanc, 2007. "On the Starting and Stopping Problem: Application in Reversible Investments," Mathematics of Operations Research, INFORMS, vol. 32(1), pages 182-192, February.
    5. De Angelis, Tiziano & Ferrari, Giorgio, 2014. "A stochastic partially reversible investment problem on a finite time-horizon: Free-boundary analysis," Stochastic Processes and their Applications, Elsevier, vol. 124(12), pages 4080-4119.
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    Cited by:

    1. Randall Martyr, 2016. "Finite-Horizon Optimal Multiple Switching with Signed Switching Costs," Mathematics of Operations Research, INFORMS, vol. 41(4), pages 1432-1447, November.

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