Quadratic BSDEs with double constraints driven by G-Brownian motion

TL;DR

This paper studies quadratic backward stochastic differential equations driven by G-Brownian motion with double constraints, establishing their existence and uniqueness using advanced probabilistic and analytical techniques.

Contribution

It introduces a novel framework for well-posedness of quadratic G-BSDEs with double mean reflections, employing G-BMO martingale representation and fixed point methods.

Findings

Proves existence and uniqueness of solutions under bounded terminal conditions.

Extends results to unbounded terminal conditions.

Develops new techniques for handling double constraints in G-BSDEs.

Abstract

In this paper, we investigate the well-posedness of quadratic backward stochastic differential equations driven by G-Brownian motion (referred to as G-BSDEs) with double mean reflections. By employing a representation of the solution via G-BMO martingale techniques, along with fixed point arguments, the Skorokhod problem, the backward Skorokhod problem, and the {\theta}-method, we establish existence and uniqueness results for such G-BSDEs under both bounded and unbounded terminal conditions.