Maxitive monetary risk measures: worst-case risk assessment and sharp large deviations
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866916689408425984 |
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| author | Zapata, José Miguel |
| author_facet | Zapata, José Miguel |
| contents | In decision making under uncertainty and risk, worst-case risk assessments are often conducted using maxitive monetary risk measures. In this article, we study maxitive monetary risk measures on the space $L^0$ of all random variables identified modulo almost sure equality. We prove that a monetary risk measure is maxitive and continuous from below if and only if it is a penalized maximum loss. Furthermore, we characterize the maximum loss as the unique maxitive and law-invariant monetary risk measure. We apply the results to large deviation theory by providing a general criterion to establish a sharp large deviation estimate for sequences of probability measures. We use these findings to provide a formula for the asymptotics of the distortion-exponential insurance premium principle under risk pooling. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_17245 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Maxitive monetary risk measures: worst-case risk assessment and sharp large deviations Zapata, José Miguel Probability In decision making under uncertainty and risk, worst-case risk assessments are often conducted using maxitive monetary risk measures. In this article, we study maxitive monetary risk measures on the space $L^0$ of all random variables identified modulo almost sure equality. We prove that a monetary risk measure is maxitive and continuous from below if and only if it is a penalized maximum loss. Furthermore, we characterize the maximum loss as the unique maxitive and law-invariant monetary risk measure. We apply the results to large deviation theory by providing a general criterion to establish a sharp large deviation estimate for sequences of probability measures. We use these findings to provide a formula for the asymptotics of the distortion-exponential insurance premium principle under risk pooling. |
| title | Maxitive monetary risk measures: worst-case risk assessment and sharp large deviations |
| topic | Probability |
| url | https://arxiv.org/abs/2211.17245 |