A general existence and uniqueness result on multidimensional BSDEs

TL;DR

This paper proves a new existence and uniqueness theorem for multidimensional backward stochastic differential equations (BSDEs) with generators under weak monotonicity and general growth conditions, extending previous results.

Contribution

It introduces a generalized framework for existence and uniqueness of solutions to multidimensional BSDEs under weaker conditions than previously established.

Findings

Established existence and uniqueness under weak monotonicity.

Extended previous results to more general growth conditions.

Generalized the theoretical understanding of multidimensional BSDEs.

Abstract

This paper establishes a new existence and uniqueness result of solutions for multidimensional backward stochastic differential equations (BSDEs) whose generators satisfy a weak monotonicity condition and a general growth condition in $y$, which generalizes the corresponding results in [2], [3] and [5].