Doubly Reflected Backward SDEs Driven by $G$-Brownian Motion with Quadratic Generator
Probability
2026-04-28 v1
Abstract
In this paper, we study the doubly reflected backward stochastic differential equations driven by -Brownian motion (-BSDEs for short) when the generator has quadratic growth in the -component. Based on the theory of -BMO martingale and -Girsanov theorem, we establish the existence and uniqueness result when the upper obstacle is almost a generalized -It\^{o}'s process. Moreover, the solution can be approximated monotonically by the solutions to a family of penalized reflected -BSDEs with a lower obstacle, which plays an important role to establish the relation between doubly reflected -BSDEs and fully nonlinear partial differential equations with double obstacles.
Keywords
Cite
@article{arxiv.2604.23656,
title = {Doubly Reflected Backward SDEs Driven by $G$-Brownian Motion with Quadratic Generator},
author = {Hanwu Li and Peng Luo and Mengbo Zhu},
journal= {arXiv preprint arXiv:2604.23656},
year = {2026}
}