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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2407.17768 |
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| _version_ | 1866914886522503168 |
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| author | Gu, Zihao Zhao, Hui |
| author_facet | Gu, Zihao Zhao, Hui |
| contents | In this paper, we study a collection of mean-reflected backward stochastic differential equations driven by $G$-Brownian motions ($G$-BSDEs), where $G$-expectations are constrained in some time-dependent intervals. To establish well-posedness results, we firstly construct a backward Skorokhod problem with sublinear expectation, and then apply that in the study of doubly mean-reflected $G$-BSDEs involving Lipschitz and quadratic generators under bounded and unbounded terminal conditions. Also we utilize fixed-point argumentations and $θ$-methods while solving these equations. Finally, we extend the results to multi-dimensional doubly mean-reflected $G$-BSDEs with diagonal generators. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_17768 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | $G$-BSDEs with mean constraints in time-dependent intervals Gu, Zihao Zhao, Hui Probability In this paper, we study a collection of mean-reflected backward stochastic differential equations driven by $G$-Brownian motions ($G$-BSDEs), where $G$-expectations are constrained in some time-dependent intervals. To establish well-posedness results, we firstly construct a backward Skorokhod problem with sublinear expectation, and then apply that in the study of doubly mean-reflected $G$-BSDEs involving Lipschitz and quadratic generators under bounded and unbounded terminal conditions. Also we utilize fixed-point argumentations and $θ$-methods while solving these equations. Finally, we extend the results to multi-dimensional doubly mean-reflected $G$-BSDEs with diagonal generators. |
| title | $G$-BSDEs with mean constraints in time-dependent intervals |
| topic | Probability |
| url | https://arxiv.org/abs/2407.17768 |