  In actuarial research, a task of particular interest and importance is to
predict the loss cost for individual risks so that informative decisions are
made in various insurance operations such as underwriting, ratemaking, and
capital management. The loss cost is typically viewed to follow a compound
distribution where the summation of the severity variables is stopped by the
frequency variable. A challenging issue in modeling such outcome is to
accommodate the potential dependence between the number of claims and the size
of each individual claim. In this article, we introduce a novel regression
framework for compound distributions that uses a copula to accommodate the
association between the frequency and the severity variables, and thus allows
for arbitrary dependence between the two components. We further show that the
new model is very flexible and is easily modified to account for incomplete
data due to censoring or truncation. The flexibility of the proposed model is
illustrated using both simulated and real data sets. In the analysis of
granular claims data from property insurance, we find substantive negative
relationship between the number and the size of insurance claims. In addition,
we demonstrate that ignoring the frequency-severity association could lead to
biased decision-making in insurance operations.
