Asymptotic Results for Conditional Measures of Association of a Random Sum

20 Pages Posted: 20 Jul 2014 Last revised: 8 Feb 2018

See all articles by Alexandru Vali Asimit

Alexandru Vali Asimit

Cass Business School, City, University of London

Yiqing Chen

Drake University

Date Written: October 27, 2014

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 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

Asimit, Alexandru Vali and Chen, Yiqing, Asymptotic Results for Conditional Measures of Association of a Random Sum (October 27, 2014). Insurance: Mathematics and Economics, 2015, Volume 60, p.11-18 . Available at SSRN: https://ssrn.com/abstract=2468601 or http://dx.doi.org/10.2139/ssrn.2468601

Alexandru Vali Asimit (Contact Author)

Cass Business School, City, University of London ( email )

106 Bunhill Row
London, EC1Y 8TZ
United Kingdom

Yiqing Chen

Drake University ( email )

2507 University Avenue
Des Moines, IA 50311-4505
United States
5152713117 (Phone)

HOME PAGE: http://faculty.cbpa.drake.edu/acts/yiqing.chen/

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