Set-valued Star-Shaped Risk Measures
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866912239473131520 |
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| author | Nie, Bingchu Tian, Dejian Jiang, Long |
| author_facet | Nie, Bingchu Tian, Dejian Jiang, Long |
| contents | In this paper, we introduce a new class of set-valued risk measures, named set-valued star-shaped risk measures. Motivated by the results of scalar monetary and star-shaped risk measures, this paper investigates the representation theorems in the set-valued framework. It is demonstrated that set-valued risk measures can be represented as the union of a family of set-valued convex risk measures, and set-valued normalized star-shaped risk measures can be represented as the union of a family of set-valued normalized convex risk measures. The link between set-valued risk measures and set-valued star-shaped risk measures is also established. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_18014 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Set-valued Star-Shaped Risk Measures Nie, Bingchu Tian, Dejian Jiang, Long Risk Management 91G70 In this paper, we introduce a new class of set-valued risk measures, named set-valued star-shaped risk measures. Motivated by the results of scalar monetary and star-shaped risk measures, this paper investigates the representation theorems in the set-valued framework. It is demonstrated that set-valued risk measures can be represented as the union of a family of set-valued convex risk measures, and set-valued normalized star-shaped risk measures can be represented as the union of a family of set-valued normalized convex risk measures. The link between set-valued risk measures and set-valued star-shaped risk measures is also established. |
| title | Set-valued Star-Shaped Risk Measures |
| topic | Risk Management 91G70 |
| url | https://arxiv.org/abs/2402.18014 |