Beyond the Pearson correlation: heavy-tailed risks, weighted Gini correlations, and a Gini-type weighted insurance pricing model

TL;DR

This paper explores Gini-type correlation coefficients as alternatives to Pearson correlation in heavy-tailed distributions, establishing their relationship and introducing a Gini-weighted insurance pricing model suitable for such scenarios.

Contribution

It establishes a connection between Gini-type and Pearson correlations through regression equations and introduces a new Gini-weighted insurance pricing model for heavy-tailed risks.

Findings

Gini-type correlations relate to Pearson correlations via regression equations.

The Gini-weighted insurance model performs well with heavy-tailed distributions.

Illustrations include elliptical and Pareto distribution examples.

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, then these coefficients are related and sometimes even coincide. In general, understanding how the correlation coefficients above 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 situation 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.