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

E.H. Essaky, M. Hassani and C.E. Rhazlane

Stochastic Processes and their Applications, 2023, vol. 163, issue C, 473-497

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.

Keywords: Doubly reflected backward stochastic differential equation; Stochastic quadratic growth; Comparison theorem; Penalization method; Snell envelope (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1016/j.spa.2023.06.012

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