Large Deviations and Ruin Probabilities in Heavy-Tailed Distributions
Research Paper#Probability Theory, Extreme Value Theory, Insurance Risk🔬 Research|Analyzed: Jan 3, 2026 15:37•
Published: Dec 30, 2025 17:02
•1 min read
•ArXivAnalysis
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.
Key Takeaways
- •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.
Reference / Citation
View Original"The paper derives the polynomial rate of decay of ruin probabilities in insurance portfolios where insolvency is driven by a single extreme claim."