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In actuarial research, a task of particular interest and importance is topredict the loss cost for individual risks so that informative decisions aremade in various insurance operations such as underwriting, ratemaking, andcapital management. The loss cost is typically viewed to follow a compounddistribution where the summation of the severity variables is stopped by thefrequency variable. A challenging issue in modeling such outcome is toaccommodate the potential dependence between the number of claims and the sizeof each individual claim. In this article, we introduce a novel regressionframework for compound distributions that uses a copula to accommodate theassociation between the frequency and the severity variables, and thus allowsfor arbitrary dependence between the two components. We further show that thenew model is very flexible and is easily modified to account for incompletedata due to censoring or truncation. The flexibility of the proposed model isillustrated using both simulated and real data sets. In the analysis ofgranular claims data from property insurance, we find substantive negativerelationship between the number and the size of insurance claims. In addition,we demonstrate that ignoring the frequency-severity association could lead tobiased decision-making in insurance operations.

Regression for Copula-linked Compound Distributions with Applications in Modeling Aggregate Insurance Claims