Bounds on Multivariate Kendall’s Tau and Spearman’s Rho for Zero-Inflated Continuous Variables and their Application to Insurance

In this note, we derive upper bounds on Kendall’s tau and Spearman’s rho for multivariate zero-inflated continuous variables often encountered in insurance. A lower bound for Spearman’s rho is also established in the bivariate case. These bounds are easy to compute and can be estimated from a data set of zero-inflated random vectors as illustrated in this note with a motor insurance portfolio.