Some properties of G-SVIEs

TL;DR

This paper studies the solvability and properties of G-Backward Stochastic Volterra Integral Equations (G-SVIEs), establishing existence, uniqueness, and continuity of solutions under various Lipschitz conditions.

Contribution

It introduces new solvability results for G-SVIEs with time-varying and integral-Lipschitz coefficients using Picard iteration, and analyzes solution continuity.

Findings

Existence and uniqueness of solutions under time-varying Lipschitz conditions.

Existence and uniqueness under integral-Lipschitz conditions.

Proved continuity of solutions with respect to parameters.

Abstract

In this paper, we investigated the solvability of G-SVIEs under two cases: time-varying Lipschitz coefficients and integral-Lipschitz coefficients. Using the Picard iteration method, we established the existence and uniqueness of solutions to G-SVIEs under these two conditions. Additionally, we prove the continuity of the solution with respect to parameters in parameter-dependent G-SVIEs with Lipschitz coefficients.