  Several collective risk models have recently been proposed by relaxing the
widely used but controversial assumption of independence between claim
frequency and severity. Approaches include the bivariate copula model, random
effect model, and two-part frequency-severity model. This study focuses on the
copula approach to develop collective risk models that allow a flexible
dependence structure for frequency and severity. We first revisit the bivariate
copula method for frequency and average severity. After examining the inherent
difficulties of the bivariate copula model, we alternatively propose modeling
the dependence of frequency and individual severities using multivariate
Gaussian and t-copula functions. The proposed copula models have computational
advantages and provide intuitive interpretations for the dependence structure.
Our analytical findings are illustrated by analyzing automobile insurance data.
