City Research Online

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


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
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:
Text - Accepted Version
Available under License : See the attached licence file.

Download (188kB) | Preview
Text (Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International Licence) - Other
Download (202kB) | Preview



Downloads per month over past year

View more statistics

Actions (login required)

Admin Login Admin Login