Existence of global solutions for multi-dimensional coupled FBSDEs with diagonally quadratic generators

TL;DR

This paper establishes conditions for the existence of global solutions to multi-dimensional coupled forward-backward stochastic differential equations with diagonally quadratic generators, and also provides a comparison result for these solutions.

Contribution

It introduces new conditions ensuring global solutions for multi-dimensional coupled FBSDEs with diagonally quadratic generators and extends comparison results to these solutions.

Findings

Existence of global solutions under specific conditions.

Comparison results for the solutions.

Extension of known results to multi-dimensional cases.

Abstract

The present paper is devoted to study multi-dimensional coupled FBSDEs with diagonally quadratic generators. Relying on a comparison result obtained in [20], we provide conditions under which there exists a global solution. As a byproduct, we further give a comparison result for this global solution.