Time-Delayed Generalized BSDEs
Fuente:
arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2020
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866908674252865536 |
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| author | Di Persio, Luca Garbelli, Matteo Maticiuc, Lucian Zălinescu, Adrian |
| author_facet | Di Persio, Luca Garbelli, Matteo Maticiuc, Lucian Zălinescu, Adrian |
| contents | We prove the existence and uniqueness of the solution of a BSDE with time-delayed generators in the small delay setting (or equivalently small Lipschitz constant), which employs the Stieltjes integral with respect to an increasing continuous stochastic process. Moreover, we obtain a result of continuity of the solution with regard to the increasing process, assuming only uniform convergence, but not in variation. We also prove the existence in the case of an arbitrary delay by imposing monotonicity and linearity on generators. Lastly, we provide an application of the theoretical framework within an insurance based example. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2012_00798 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Time-Delayed Generalized BSDEs Di Persio, Luca Garbelli, Matteo Maticiuc, Lucian Zălinescu, Adrian Probability 60H10, 60H30 We prove the existence and uniqueness of the solution of a BSDE with time-delayed generators in the small delay setting (or equivalently small Lipschitz constant), which employs the Stieltjes integral with respect to an increasing continuous stochastic process. Moreover, we obtain a result of continuity of the solution with regard to the increasing process, assuming only uniform convergence, but not in variation. We also prove the existence in the case of an arbitrary delay by imposing monotonicity and linearity on generators. Lastly, we provide an application of the theoretical framework within an insurance based example. |
| title | Time-Delayed Generalized BSDEs |
| topic | Probability 60H10, 60H30 |
| url | https://arxiv.org/abs/2012.00798 |