Reflected Advanced Backward Stochastic Differential Equations with Default

TL;DR

This paper studies reflected advanced backward stochastic differential equations with default risk, establishing existence, uniqueness, a comparison theorem, and linking them to optimal stopping problems in an enlarged filtration setting.

Contribution

It introduces a framework for RABSDE with default, proving key properties and connecting them to optimal stopping, which advances the understanding of stochastic control under default risk.

Findings

Unique solution existence for RABSDE with default

Comparison theorem established for these equations

Connection to optimal stopping problems demonstrated

Abstract

We are interested on reflected advanced backward stochastic differential equations (RABSDE) with default. By the predictable representation property and for a Lipschitz driver, we show that the RABSDE with default has a unique solution in the enlarged filtration. A comparison theorem for such type of equations is proved. Finally, we give a connection between RABSDE and optimal stopping.