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Dynkin games with Poisson random intervention times

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  • Gechun Liang
  • Haodong Sun

Abstract

This paper introduces a new class of Dynkin games, where the two players are allowed to make their stopping decisions at a sequence of exogenous Poisson arrival times. The value function and the associated optimal stopping strategy are characterized by the solution of a backward stochastic differential equation. The paper further applies the model to study the optimal conversion and calling strategies of convertible bonds, and their asymptotics when the Poisson intensity goes to infinity.

Suggested Citation

  • Gechun Liang & Haodong Sun, 2018. "Dynkin games with Poisson random intervention times," Papers 1803.00329, arXiv.org, revised Jul 2019.
    • Handle: RePEc:arx:papers:1803.00329
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    File URL: http://arxiv.org/pdf/1803.00329
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    References listed on IDEAS

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    1. Erhan Bayraktar & Song Yao, 2015. "On the Robust Dynkin Game," Papers 1506.09184, arXiv.org, revised Sep 2016.
    2. Touzi, N. & Vieille, N., 1999. "Continuous-Time Dynkin Games with Mixed Strategies," Papiers d'Economie Mathématique et Applications 1999.112, Université Panthéon-Sorbonne (Paris 1).
    3. Dinah Rosenberg & Eilon Solan & Nicolas Vieille, 1999. "Stopping Games with Randomized Strategies," Discussion Papers 1258, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    4. Huiwen Yan & Zhou Yang & Fahuai Yi & Gechun Liang, 2015. "Dynkin Game of Convertible Bonds and Their Optimal Strategy," Papers 1503.08961, arXiv.org.
    5. Tomasz Bielecki & Stephane Crepey & Monique Jeanblanc & Marek Rutkowski, 2008. "Arbitrage pricing of defaultable game options with applications to convertible bonds," Quantitative Finance, Taylor & Francis Journals, vol. 8(8), pages 795-810.
    6. Ingersoll, Jonathan Jr., 1977. "A contingent-claims valuation of convertible securities," Journal of Financial Economics, Elsevier, vol. 4(3), pages 289-321, May.
    7. Brennan, M J & Schwartz, Eduardo S, 1977. "Convertible Bonds: Valuation and Optimal Strategies for Call and Conversion," Journal of Finance, American Finance Association, vol. 32(5), pages 1699-1715, December.
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    Cited by:

    1. David Hobson & Gechun Liang & Edward Wang, 2021. "Callable convertible bonds under liquidity constraints and hybrid priorities," Papers 2111.02554, arXiv.org, revised Oct 2024.
    2. Gechun Liang & Wei Wei & Zhen Wu & Zhenda Xu, 2024. "Recursive Optimal Stopping with Poisson Stopping Constraints," Papers 2407.17975, arXiv.org.
    3. Alvarez E., Luis H.R. & Lempa, Jukka & Saarinen, Harto & Sillanpää, Wiljami, 2024. "Solutions for Poissonian stopping problems of linear diffusions via extremal processes," Stochastic Processes and their Applications, Elsevier, vol. 172(C).

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