Existence and uniqueness are proven for doubly reflected G-BSDEs with quadratic generators when the upper obstacle is nearly a generalized G-Itô process, along with a penalization approximation and PDE link.
and Hu, Y.: Quadratic BSDEs with convex generators and unbounded terminal conditions.Probab
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Doubly Reflected Backward SDEs Driven by $G$-Brownian Motion with Quadratic Generator
Existence and uniqueness are proven for doubly reflected G-BSDEs with quadratic generators when the upper obstacle is nearly a generalized G-Itô process, along with a penalization approximation and PDE link.