# A class of multidimensional quadratic BSDEs

## TL;DR

This paper investigates a specific class of multidimensional quadratic backward stochastic differential equations (BSDEs), establishing existence and uniqueness results under certain conditions, and extends these findings to related one-dimensional and lower triangular cases.

## Contribution

It introduces new existence and uniqueness results for a class of multidimensional quadratic BSDEs with product generators, expanding the theoretical understanding of such equations.

## Key findings

- Existence of solutions for the multidimensional quadratic BSDEs under parameter constraints.
- Uniqueness of solutions in the one-dimensional case with bounded terminal values.
- Existence of solutions for lower triangular quadratic BSDEs with bounded terminal values.

## Abstract

In this paper we study a multidimensional quadratic BSDE with a particular class of product generators and give a result of existence of solution in a suitable complete metric space under some constraints on parameters. We also use that result to derive the existence and uniqueness of solution to the one dimensional case with bounded terminal values and show the existence of solution to a lower triangular quadratic BSDE with certain bounded terminal values.