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Reflected BSDEs with jumps in time-dependent convex càdlàg domains

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  • Eddahbi, M’hamed
  • Fakhouri, Imade
  • Ouknine, Youssef

Abstract

In the first part of the paper, we study the unique solvability of multidimensional reflected backward stochastic differential equations (RBSDEs) of Wiener–Poisson type with reflection in the inward spatial normal direction of a time-dependent adapted càdlàg convex set D={Dt,t∈[0,T]}. The existence result is obtained by approximating the solutions of this class of RBSDEs by solutions of BSDEs with reflection in discretizations of D, while the uniqueness is established by using Itô’s formula. In the second part of the paper, we show that the solutions of our RBSDEs can be approximated via a non-standard penalization method.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:130:y:2020:i:11:p:6515-6555
    DOI: 10.1016/j.spa.2020.06.001
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    References listed on IDEAS

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    1. Hamadène, Said & Zhang, Jianfeng, 2010. "Switching problem and related system of reflected backward SDEs," Stochastic Processes and their Applications, Elsevier, vol. 120(4), pages 403-426, April.
    2. Klimsiak, Tomasz, 2015. "Reflected BSDEs on filtered probability spaces," Stochastic Processes and their Applications, Elsevier, vol. 125(11), pages 4204-4241.
    3. Hamadène, S. & Wang, H., 2009. "BSDEs with two RCLL reflecting obstacles driven by Brownian motion and Poisson measure and a related mixed zero-sum game," Stochastic Processes and their Applications, Elsevier, vol. 119(9), pages 2881-2912, September.
    4. Aazizi, Soufiane & El Mellali, Tarik & Fakhouri, Imade & Ouknine, Youssef, 2018. "Optimal switching problem and related system of BSDEs with left-Lipschitz coefficients and mixed reflections," Statistics & Probability Letters, Elsevier, vol. 137(C), pages 70-78.
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