$\mathbb{L}^p$-solutions for BSDEs and Reflected BSDEs with jumps in a general filtration under stochastic Lipschitz coefficient
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909730965815296 |
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| author | Elmansouri, Badr |
| author_facet | Elmansouri, Badr |
| contents | In this paper, we study the existence and uniqueness of $\mathbb{L}^p$-solutions for $p \in (1, 2)$, first for backward stochastic differential equations (BSDEs) in a general filtration that supports a Brownian motion and an independent Poisson random measure, and then for reflected BSDEs with an RCLL barrier in the same stochastic framework. The results are obtained under suitable $\mathbb{L}^p$-integrability conditions on the data and a stochastic-Lipschitz condition on the coefficient. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_07039 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $\mathbb{L}^p$-solutions for BSDEs and Reflected BSDEs with jumps in a general filtration under stochastic Lipschitz coefficient Elmansouri, Badr Probability 60H10, 60H15, 60H30 In this paper, we study the existence and uniqueness of $\mathbb{L}^p$-solutions for $p \in (1, 2)$, first for backward stochastic differential equations (BSDEs) in a general filtration that supports a Brownian motion and an independent Poisson random measure, and then for reflected BSDEs with an RCLL barrier in the same stochastic framework. The results are obtained under suitable $\mathbb{L}^p$-integrability conditions on the data and a stochastic-Lipschitz condition on the coefficient. |
| title | $\mathbb{L}^p$-solutions for BSDEs and Reflected BSDEs with jumps in a general filtration under stochastic Lipschitz coefficient |
| topic | Probability 60H10, 60H15, 60H30 |
| url | https://arxiv.org/abs/2508.07039 |