Multivalued backward stochastic differential equations with jumps and moving boundary
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866912731093794816 |
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| author | Elmansouri, Badr Ouknine, Anas Ouknine, Youssef |
| author_facet | Elmansouri, Badr Ouknine, Anas Ouknine, Youssef |
| contents | We prove existence and uniqueness for a one-dimensional multivalued backward stochastic differential equation with jumps. The equation involves a time-indexed family of maximal monotone operators $k_t(\cdot)$ associated with increasing functions $k(t,\cdot)$ taking values in $\mathbb{R}_-$ and having domains that are intervals with time-dependent boundaries. Existence is obtained by a penalization method under a Lipschitz condition on the driver in $(y,z)$, a monotonicity condition in the jump parameter $ψ$, square-integrability of the terminal condition and the driver, and local-in-time integrability conditions on $k(\cdot,y)$. We also address the extension to the case where the operators $k_t(\cdot)$ act on unbounded intervals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_21679 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Multivalued backward stochastic differential equations with jumps and moving boundary Elmansouri, Badr Ouknine, Anas Ouknine, Youssef Probability 60H05, 60H10, 60H30, 47H05 We prove existence and uniqueness for a one-dimensional multivalued backward stochastic differential equation with jumps. The equation involves a time-indexed family of maximal monotone operators $k_t(\cdot)$ associated with increasing functions $k(t,\cdot)$ taking values in $\mathbb{R}_-$ and having domains that are intervals with time-dependent boundaries. Existence is obtained by a penalization method under a Lipschitz condition on the driver in $(y,z)$, a monotonicity condition in the jump parameter $ψ$, square-integrability of the terminal condition and the driver, and local-in-time integrability conditions on $k(\cdot,y)$. We also address the extension to the case where the operators $k_t(\cdot)$ act on unbounded intervals. |
| title | Multivalued backward stochastic differential equations with jumps and moving boundary |
| topic | Probability 60H05, 60H10, 60H30, 47H05 |
| url | https://arxiv.org/abs/2511.21679 |