Large Deviations and Ruin Probabilities in Heavy-Tailed Distributions

This paper provides a significant contribution to the understanding of extreme events in heavy-tailed distributions. The results on large deviation asymptotics for the maximum order statistic are crucial for analyzing exceedance probabilities beyond standard extreme-value theory. The application to ruin probabilities in insurance portfolios highlights the practical relevance of the theoretical findings, offering insights into solvency risk.

• •Establishes sharp large deviation asymptotics for the maximum order statistic of heavy-tailed random variables.
• •Provides exact decay rates for exceedance probabilities at thresholds exceeding extreme-value scaling.
• •Applies the findings to derive the polynomial rate of decay of ruin probabilities in insurance portfolios.