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Doubly reflected BSDEs with stochastic quadratic growth: Around the predictable obstacles

Author

Listed:
  • Essaky, E.H.
  • Hassani, M.
  • Rhazlane, C.E.

Abstract

We prove the existence of maximal (and minimal) solution for one-dimensional generalized doubly reflected backward stochastic differential equation (RBSDE for short) with irregular barriers and stochastic quadratic growth, for which the solution Y has to remain between two rcll barriers L and U on [0,T[, and its left limit Y− has to stay respectively above and below two predictable barriers l and u on ]0,T]. This is done without assuming any P−integrability conditions and under weaker assumptions on the input data. In particular, we construct a maximal solution for such a RBSDE when the terminal condition ξ is only FT−measurable and the driver f is continuous with general growth with respect to the variable y and stochastic quadratic growth with respect to the variable z.

Suggested Citation

  • Essaky, E.H. & Hassani, M. & Rhazlane, C.E., 2023. "Doubly reflected BSDEs with stochastic quadratic growth: Around the predictable obstacles," Stochastic Processes and their Applications, Elsevier, vol. 163(C), pages 473-497.
    • Handle: RePEc:eee:spapps:v:163:y:2023:i:c:p:473-497
    DOI: 10.1016/j.spa.2023.06.012
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    References listed on IDEAS

    as
    1. Bayraktar, Erhan & Yao, Song, 2015. "Doubly reflected BSDEs with integrable parameters and related Dynkin games," Stochastic Processes and their Applications, Elsevier, vol. 125(12), pages 4489-4542.
    2. Essaky, E.H. & Hassani, M. & Ouknine, Y., 2015. "Stochastic quadratic BSDE with two RCLL obstacles," Stochastic Processes and their Applications, Elsevier, vol. 125(6), pages 2147-2189.
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