Existence and uniqueness of solutions for multi-dimensional reflected BSDEs with diagonally quadratic generators

TL;DR

This paper establishes the existence and uniqueness of solutions for multi-dimensional reflected backward stochastic differential equations with diagonally quadratic generators, using recent comparison theorems and penalization methods.

Contribution

It introduces new existence and uniqueness results for a class of multi-dimensional reflected BSDEs with diagonally quadratic generators, extending previous work.

Findings

Proves existence and uniqueness of solutions.

Provides a comparison theorem for these BSDEs.

Uses penalization method for proofs.

Abstract

In this paper, we study multi-dimensional reflected backward stochastic differential equations with diagonally quadratic generators. Using the comparison theorem for diagonally quadratic BSDEs which is established recently in [14], we obtain the existence and uniqueness of a solution by a penalization method. Moreover, we provide a comparison theorem.