Sharp large deviation estimates for heavy-tailed extrema
Probability
2026-01-09 v2
Abstract
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.
Cite
@article{arxiv.2512.24352,
title = {Sharp large deviation estimates for heavy-tailed extrema},
author = {José M. Zapata},
journal= {arXiv preprint arXiv:2512.24352},
year = {2026}
}