Mean-reflected $G$-BSDEs with multi-variate constraints

TL;DR

This paper investigates multi-dimensional reflected G-BSDEs with multivariate constraints under G-expectation, establishing existence and uniqueness results for solutions with diagonally dependent generators.

Contribution

It introduces a new framework for multi-dimensional G-BSDEs with multivariate constraints and proves existence and uniqueness using fixed-point methods.

Findings

Established existence and uniqueness of solutions.

Handled multi-variate constraints on G-expectation.

Analyzed diagonally dependent generators.

Abstract

In this paper, we study the multi-dimensional reflected backward stochastic differential equation driven by $G$-Brownian motion ($G$-BSDE) with a multi-variate constraint on the $G$-expectation of its solution. The generators are diagonally dependent on $Z$ and on all $Y$-components. We obtain the existence and uniqueness result via a fixed-point argumentation.