Well-posedness of quadratic RBSDEs and BSDEs with one-sided growth restrictions

Shiqiu Zheng

Stochastic Processes and their Applications, 2026, vol. 199, issue C

Abstract: In this paper, we investigate the well-posedness of bounded and unbounded solutions for reflected backward stochastic differential equations (RBSDEs) and backward stochastic differential equations (BSDEs). The generators of these equations satisfy a one-sided growth restriction on the variable y and have a general quadratic growth in the variable z. The solutions Yt (and the obstacles for RBSDEs) take values in either R or (0, ∞). We obtain the existence of solutions primarily by using the methods from Essaky and Hassani (2011) and Bahlali et al. (2017). For the uniqueness of solutions, we provide a method applicable when the generators are convex in (y, z) or are (locally) Lipschitz in y and convex in z. Our method relies on the θ-difference technique introduced by Briand and Hu (2008), and some novel comparison arguments based on RBSDEs. We also establish some general comparison theorems for such RBSDEs and BSDEs.

Keywords: Reflected backward stochastic differential equation; Backward stochastic differential equation; Comparison theorem; Quadratic growth; One-sided growth (search for similar items in EconPapers)
Date: 2026
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DOI: 10.1016/j.spa.2026.104972

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