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BEYOND THE PEARSON CORRELATION: HEAVY-TAILED RISKS, WEIGHTED GINI CORRELATIONS, AND A GINI-TYPE WEIGHTED INSURANCE PRICING MODEL

Published online by Cambridge University Press:  07 August 2017

Edward Furman  and
Ričardas Zitikis
Edward Furman*
Affiliation:
Department of Mathematics and Statistics, York University, Toronto, Ontario M3J 1P3, Canada
Ričardas Zitikis
Affiliation:
Department of Statistical and Actuarial Sciences, University of Western Ontario, London, Ontario N6A 5B7, Canada, E-Mail: zitikis@stats.uwo.ca
*
E-Mail: efurman@mathstat.yorku.ca
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Abstract

Gini-type correlation coefficients have become increasingly important in a variety of research areas, including economics, insurance and finance, where modelling with heavy-tailed distributions is of pivotal importance. In such situations, naturally, the classical Pearson correlation coefficient is of little use. On the other hand, it has been observed that when light-tailed situations are of interest, and hence when both the Gini-type and Pearson correlation coefficients are well defined and finite, these coefficients are related and sometimes even coincide. In general, understanding how these correlation coefficients are related has been an illusive task. In this paper, we put forward arguments that establish such a connection via certain regression-type equations. This, in turn, allows us to introduce a Gini-type weighted insurance pricing model that works in heavy-tailed situations and thus provides a natural alternative to the classical capital asset pricing model. We illustrate our theoretical considerations using several bivariate distributions, such as elliptical and those with heavy-tailed Pareto margins.

Keywords

Pearson correlationweighted Gini correlationcapital asset pricing modelweighted insurance pricing modelbivariate distributions
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 47 , Issue 3 , September 2017 , pp. 919 - 942
Copyright
Copyright © Astin Bulletin 2017 

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