Asymptotic results for conditional measures of association of a random sum

Alexandru V. Asimit and Yiqing Chen

Insurance: Mathematics and Economics, 2015, vol. 60, issue C, 11-18

Abstract: 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 the tail index of the underlying distribution.

Keywords: Extreme Value Theory; Long-tailed distribution; Gumbel tail; Kendall’s tau; Order statistics; Pearson product-moment correlation coefficient; Regular variation; Spearman’s rho (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:60:y:2015:i:c:p:11-18

DOI: 10.1016/j.insmatheco.2014.10.012

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