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BSDEs with two RCLL Reflecting Obstacles driven by a Brownian Motion and Poisson Measure and related Mixed Zero-Sum Games

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  • S. Hamad'ene
  • H. Wang

Abstract

In this paper we study Backward Stochastic Differential Equations with two reflecting right continuous with left limits obstacles (or barriers) when the noise is given by Brownian motion and a Poisson random measure mutually independent. The jumps of the obstacle processes could be either predictable or inaccessible. We show existence and uniqueness of the solution when the barriers are completely separated and the generator uniformly Lipschitz. We do not assume the existence of a difference of supermartingales between the obstacles. As an application, we show that the related mixed zero-sum differential-integral game problem has a value.

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  • S. Hamad'ene & H. Wang, 2008. "BSDEs with two RCLL Reflecting Obstacles driven by a Brownian Motion and Poisson Measure and related Mixed Zero-Sum Games," Papers 0803.1815, arXiv.org.
    • Handle: RePEc:arx:papers:0803.1815
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    Cited by:

    1. Klimsiak, Tomasz, 2015. "Reflected BSDEs on filtered probability spaces," Stochastic Processes and their Applications, Elsevier, vol. 125(11), pages 4204-4241.
    2. Monia Karouf, 2019. "Reflected and Doubly Reflected Backward Stochastic Differential Equations with Time-Delayed Generators," Journal of Theoretical Probability, Springer, vol. 32(1), pages 216-248, March.
    3. Eddahbi, M’hamed & Fakhouri, Imade & Ouknine, Youssef, 2020. "Reflected BSDEs with jumps in time-dependent convex càdlàg domains," Stochastic Processes and their Applications, Elsevier, vol. 130(11), pages 6515-6555.
    4. Klimsiak, Tomasz, 2021. "Non-semimartingale solutions of reflected BSDEs and applications to Dynkin games," Stochastic Processes and their Applications, Elsevier, vol. 134(C), pages 208-239.
    5. Fan, Xiliang & Ren, Yong & Zhu, Dongjin, 2010. "A note on the doubly reflected backward stochastic differential equations driven by a Lévy process," Statistics & Probability Letters, Elsevier, vol. 80(7-8), pages 690-696, April.
    6. Yuri Kifer, 2012. "Dynkin Games and Israeli Options," Papers 1209.1791, arXiv.org.

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