Asymptotic Results for Conditional Measures of Association of a Random Sum
20 Pages Posted: 20 Jul 2014 Last revised: 8 Feb 2018
Date Written: October 27, 2014
Asymptotic results are obtained for several conditional measures of association. The chosen random variables are the first two order statistics and the total sum within a random sum. Many of the results have confirmed the “one-jump” property of the risk model. Non-trivial limits are obtained when the dependence among the first two order statistics is considered. Our results help in understanding the extreme behaviour of well-known reinsurance treaties that involve only few large claims. Interestingly, the Pearson product-moment correlation coefficient between the first two order statistics provides an alternative procedure to estimate tail index of the underlying distribution.
Keywords: Extreme Value Theory, Layer reinsurance, Long-Tailed Distribution, Gumbel Tail, Kendall’s tau, Order statistics, Pearson Product-Moment Correlation Coefficient, Regular Variation, Spearman’s rho, Tail index
JEL Classification: C14, C20
Suggested Citation: Suggested Citation