A note on continuity and asymptotic consistency of measures of risk and variability
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910801968758784 |
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| author | Gao, Niushan Xanthos, Foivos |
| author_facet | Gao, Niushan Xanthos, Foivos |
| contents | In this short note, we show that every convex, order bounded above functional on a Frechet lattice is automatically norm continuous. This improves a result in \cite{RS06} and applies to many deviation and variability measures. We also show that an order-continuous, law-invariant functional on an Orlicz space is strongly consistent everywhere, extending a result in \cite{KSZ14}. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_09766 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A note on continuity and asymptotic consistency of measures of risk and variability Gao, Niushan Xanthos, Foivos Risk Management 91G70, 91B30, 46E30 In this short note, we show that every convex, order bounded above functional on a Frechet lattice is automatically norm continuous. This improves a result in \cite{RS06} and applies to many deviation and variability measures. We also show that an order-continuous, law-invariant functional on an Orlicz space is strongly consistent everywhere, extending a result in \cite{KSZ14}. |
| title | A note on continuity and asymptotic consistency of measures of risk and variability |
| topic | Risk Management 91G70, 91B30, 46E30 |
| url | https://arxiv.org/abs/2405.09766 |