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

TL;DR

This paper introduces a flexible copula-based regression model for compound distributions in insurance, capturing dependence between claim frequency and severity, improving prediction accuracy and decision-making.

Contribution

A novel copula-based regression framework for modeling dependent frequency and severity in insurance claims, adaptable to incomplete data and demonstrated with real datasets.

Findings

Negative relationship between claim number and size found in property insurance data.

Ignoring frequency-severity dependence can bias insurance decision-making.

Model effectively handles censored and truncated data.

Abstract

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.