Well-posedness of reflected BSDEs with default time and irregular barrier: An application to optimal control
Probability
2026-05-07 v1
Abstract
We consider a reflected backward stochastic differential equations with default time and an optional barrier in a filtration generated by a one-dimensional Brownian motion and a defaultable process. We suppose that the barrier have trajectories with left and right finite limits. We provide the existence and uniqueness result when the coefficient is scholastic Lipschitz by using a modified penalization method. Under an additional assumption of right-upper semi-continuity along stopping times on the trajectories of the barrier, we characterize the state process for such RBSDEs as the value function of an optimal stopping problem associated with a non-linear -expectation.
Cite
@article{arxiv.2605.04359,
title = {Well-posedness of reflected BSDEs with default time and irregular barrier: An application to optimal control},
author = {Badr Elmansouri and Mohamed El Otmani},
journal= {arXiv preprint arXiv:2605.04359},
year = {2026}
}