Some apriori estimates of G-BSDEs and the G-martingale representation for a special case

TL;DR

This paper develops a priori estimates for G-BSDEs, establishes a G-martingale representation theorem under strong conditions, and proves existence and uniqueness of solutions, advancing the theoretical understanding of G-BSDEs.

Contribution

It introduces new a priori estimates for G-BSDE solutions and proves a G-martingale representation theorem under strong assumptions, which are novel contributions.

Findings

Derived integral and differential forms of G-BSDEs

Established a G-martingale representation theorem under strong conditions

Proved existence and uniqueness of G-BSDE solutions

Abstract

This paper presents the integral(or differential) form of G-BSDEs, gives some kind of apriori estimates of their solutions, and under a very strong condition, proves the G-martingale representation theorem, and the existence and uniqueness theorem of G-BSDEs.