A stability approach for solving multidimensional quadratic BSDEs

TL;DR

This paper proves existence and uniqueness for a class of multidimensional quadratic BSDEs using a stability approach, extending scalar results and providing practical examples.

Contribution

It introduces a stability-based method for solving multidimensional quadratic BSDEs, expanding the theoretical framework and applicability beyond previous scalar-focused work.

Findings

Established existence and uniqueness for the class of BSDEs.

Provided effective examples of applications.

Extended scalar quadratic BSDE techniques to multidimensional cases.

Abstract

We establish an existence and uniqueness result for a class of multidimensional quadratic backward stochastic differential equations (BSDE). This class is characterized by constraints on some uniform a priori estimate on solutions of a sequence of approximated BSDEs. We also present effective examples of applications. Our approach relies on the strategy developed by Briand and Elie in [Stochastic Process. Appl. 123 2921--2939] concerning scalar quadratic BSDEs.