Well-posedness of reflected BSDEs with default time and irregular barrier: An application to optimal control

Badr Elmansouri; Mohamed El Otmani

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arXiv · 2605.04359

Well-posedness of reflected BSDEs with default time and irregular barrier: An application to optimal control

Badr Elmansouri·Mohamed El Otmani

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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 $f$-expectation.

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Badr Elmansouri, Mohamed El Otmani. 2026-05-05. Well-posedness of reflected BSDEs with default time and irregular barrier: An application to optimal control. https://arxiv.org/abs/2605.04359

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