Asymptotic results for conditional measures of association of a random sum

Asimit, A.V. & Chen, Y. (2015). Asymptotic results for conditional measures of association of a random sum. Insurance: Mathematics and Economics, 60, pp. 11-18. doi: 10.1016/j.insmatheco.2014.10.012

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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.

Item 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/
Uncontrolled 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
Divisions: Cass Business School > Faculty of Actuarial Science & Insurance
Related URLs:
URI: http://openaccess.city.ac.uk/id/eprint/12171

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