Backward Stochastic Volterra integral equations driven by G-Brownian motion

TL;DR

This paper investigates backward stochastic Volterra integral equations driven by G-Brownian motion, establishing existence, uniqueness, and comparison results using novel iterative and G-stochastic analysis methods.

Contribution

It introduces a new backward iteration approach for G-BSVIEs and proves fundamental properties like existence, uniqueness, and comparison theorem.

Findings

Established existence and uniqueness of solutions.

Proved a comparison theorem for G-BSVIEs.

Developed a novel iterative method for analysis.

Abstract

In this paper, we study the Backward stochastic Volterra integral equation driven by G-Brownian motion (G-BSVIE). By adopting a different backward iteration method, we construct the approximating sequences on each local interval. With the help of G-stochastic analysis techniques and the monotone convergence theorem, the existence, uniqueness, and continuity of the solution over the entire interval are established. Moreover, we derive the comparison theorem.