Well-posedness of reflected BSDEs with default time and irregular barrier: An application to optimal control
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866915983600386048 |
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| author | Elmansouri, Badr Otmani, Mohamed El |
| author_facet | Elmansouri, Badr Otmani, Mohamed El |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_04359 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Well-posedness of reflected BSDEs with default time and irregular barrier: An application to optimal control Elmansouri, Badr Otmani, Mohamed El Probability 60H05, 60H15, 60H20 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. |
| title | Well-posedness of reflected BSDEs with default time and irregular barrier: An application to optimal control |
| topic | Probability 60H05, 60H15, 60H20 |
| url | https://arxiv.org/abs/2605.04359 |