  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.
