Beyond the Pearson Correlation: Heavy-Tailed Risks, Weighted Gini Correlations, and a Gini-Type Weighted Insurance Pricing Model

摘要

Gini-type correlation coefficients have become increasingly important in avariety of research areas, including economics, insurance and finance, wheremodelling with heavy-tailed distributions is of pivotal importance. In suchsituations, naturally, the classical Pearson correlation coefficient is oflittle use. On the other hand, it has been observed that when light-tailedsituations are of interest, and hence when both the Gini-type and Pearsoncorrelation coefficients are well-defined and finite, then these coefficientsare related and sometimes even coincide. In general, understanding how thecorrelation coefficients above are related has been an illusive task. In thispaper we put forward arguments that establish such a connection via certainregression-type equations. This, in turn, allows us to introduce a Gini-typeWeighted Insurance Pricing Model that works in heavy-tailed situation and thusprovides a natural alternative to the classical Capital Asset Pricing Model. Weillustrate our theoretical considerations using several bivariatedistributions, such as elliptical and those with heavy-tailed Pareto margins.