City Research Online

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.

Publication Type:	Article
Additional Information:	© 2015, Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/
Publisher Keywords:	Extreme Value Theory; Long-tailed distribution; Gumbel tail; Kendall’s tau; Order statistics; Pearson product-moment correlation coefficient; Regular variation; Spearman’s rho
Subjects:	H Social Sciences > HD Industries. Land use. Labor > HD61 Risk Management
Departments:	Bayes Business School > Actuarial Science & Insurance
Related URLs:	https://ssrn.com/abstract=2468601

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