  We present a joint copula-based model for insurance claims and sizes. It uses
bivariate copulae to accommodate for the dependence between these quantities.
We derive the general distribution of the policy loss without the restrictive
assumption of independence. We illustrate that this distribution tends to be
skewed and multi-modal, and that an independence assumption can lead to
substantial bias in the estimation of the policy loss. Further, we extend our
framework to regression models by combining marginal generalized linear models
with a copula. We show that this approach leads to a flexible class of models,
and that the parameters can be estimated efficiently using maximum-likelihood.
We propose a test procedure for the selection of the optimal copula family. The
usefulness of our approach is illustrated in a simulation study and in an
analysis of car insurance policies.
