$\mathbb{L}^p$-solutions $(1 <p< 2)$ for reflected BSDEs with general jumps and stochastic monotone generators
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866915252229111808 |
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| author | Elmansouri, Badr Otmani, Mohamed El Marzougue, Mohamed |
| author_facet | Elmansouri, Badr Otmani, Mohamed El Marzougue, Mohamed |
| contents | We consider a one-reflected backward stochastic differential equation with a general RCLL barrier in a filtration that supports a Brownian motion and an independent Poisson random measure. We establish the existence and uniqueness of a solution in $\mathbb{L}^p$ for $p \in (1,2)$. The result is obtained by means of the penalization method, under the assumption that the coefficient is stochastically monotone with respect to the state variable $y$, stochastically Lipschitz with respect to the control variables $(z,u)$, and satisfies suitable linear growth and $p$-integrability conditions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_15136 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $\mathbb{L}^p$-solutions $(1 <p< 2)$ for reflected BSDEs with general jumps and stochastic monotone generators Elmansouri, Badr Otmani, Mohamed El Marzougue, Mohamed Probability 60H10, 60H15, 60H30 We consider a one-reflected backward stochastic differential equation with a general RCLL barrier in a filtration that supports a Brownian motion and an independent Poisson random measure. We establish the existence and uniqueness of a solution in $\mathbb{L}^p$ for $p \in (1,2)$. The result is obtained by means of the penalization method, under the assumption that the coefficient is stochastically monotone with respect to the state variable $y$, stochastically Lipschitz with respect to the control variables $(z,u)$, and satisfies suitable linear growth and $p$-integrability conditions. |
| title | $\mathbb{L}^p$-solutions $(1 <p< 2)$ for reflected BSDEs with general jumps and stochastic monotone generators |
| topic | Probability 60H10, 60H15, 60H30 |
| url | https://arxiv.org/abs/2504.15136 |