Sharp large deviation estimates for heavy-tailed extrema
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918277563809792 |
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| author | Zapata, José M. |
| author_facet | Zapata, José M. |
| contents | We establish sharp large deviation asymptotics for the maximum order statistic of independent and identically distributed heavy-tailed random variables, valid for all Borel subsets of the right tail. This result yields exact decay rates for exceedance probabilities at thresholds that grow faster than the natural extreme-value scaling. As an application, we derive the polynomial rate of decay of ruin probabilities in insurance portfolios where insolvency is driven by a single extreme claim. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_24352 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Sharp large deviation estimates for heavy-tailed extrema Zapata, José M. Probability We establish sharp large deviation asymptotics for the maximum order statistic of independent and identically distributed heavy-tailed random variables, valid for all Borel subsets of the right tail. This result yields exact decay rates for exceedance probabilities at thresholds that grow faster than the natural extreme-value scaling. As an application, we derive the polynomial rate of decay of ruin probabilities in insurance portfolios where insolvency is driven by a single extreme claim. |
| title | Sharp large deviation estimates for heavy-tailed extrema |
| topic | Probability |
| url | https://arxiv.org/abs/2512.24352 |