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Optimal switching problem and related system of BSDEs with left-Lipschitz coefficients and mixed reflections

Author

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  • Aazizi, Soufiane
  • El Mellali, Tarik
  • Fakhouri, Imade
  • Ouknine, Youssef

Abstract

This paper studies a system of backward stochastic differential equations with both oblique and normal reflections which arises in the study of the optimal switching problem. The main feature of our system is that its components are interconnected through both the obstacles and the generators which are only assumed to be left-Lipschitz continuous with respect to y. We provide an existence theorem of minimal solutions for RBSDEs in this framework.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:137:y:2018:i:c:p:70-78
    DOI: 10.1016/j.spl.2018.01.006
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    References listed on IDEAS

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    1. Zheng, Shiqiu & Zhou, Shengwu, 2008. "A generalized existence theorem of reflected BSDEs with double obstacles," Statistics & Probability Letters, Elsevier, vol. 78(5), pages 528-536, April.
    2. Klimsiak, Tomasz & Rozkosz, Andrzej & Słomiński, Leszek, 2015. "Reflected BSDEs in time-dependent convex regions," Stochastic Processes and their Applications, Elsevier, vol. 125(2), pages 571-596.
    3. 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.
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    1. 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.

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