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| Main Authors: | , |
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| Format: | Preprint |
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2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2406.13539 |
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| _version_ | 1866915306461462528 |
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| author | Han, Xia Liu, Peng |
| author_facet | Han, Xia Liu, Peng |
| contents | In this paper, we investigate the robust models for $Λ$-quantiles with partial information regarding the loss distribution, where $Λ$-quantiles extend the classical quantiles by replacing the fixed probability level with a probability/loss function $Λ$. We find that, under some assumptions, the robust $Λ$-quantiles equal the $Λ$-quantiles of the extremal distributions. This finding allows us to obtain the robust $Λ$-quantiles by applying the results of robust quantiles in the literature. Our results are applied to uncertainty sets characterized by three different constraints respectively: moment constraints, probability distance constraints via the Wasserstein metric, and marginal constraints in risk aggregation. We obtain some explicit expressions for robust $Λ$-quantiles by deriving the extremal distributions for each uncertainty set. These results are applied to optimal portfolio selection under model uncertainty. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_13539 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Robust Lambda-quantiles and extremal distributions Han, Xia Liu, Peng Mathematical Finance 91G10 In this paper, we investigate the robust models for $Λ$-quantiles with partial information regarding the loss distribution, where $Λ$-quantiles extend the classical quantiles by replacing the fixed probability level with a probability/loss function $Λ$. We find that, under some assumptions, the robust $Λ$-quantiles equal the $Λ$-quantiles of the extremal distributions. This finding allows us to obtain the robust $Λ$-quantiles by applying the results of robust quantiles in the literature. Our results are applied to uncertainty sets characterized by three different constraints respectively: moment constraints, probability distance constraints via the Wasserstein metric, and marginal constraints in risk aggregation. We obtain some explicit expressions for robust $Λ$-quantiles by deriving the extremal distributions for each uncertainty set. These results are applied to optimal portfolio selection under model uncertainty. |
| title | Robust Lambda-quantiles and extremal distributions |
| topic | Mathematical Finance 91G10 |
| url | https://arxiv.org/abs/2406.13539 |