Pricing Nonlife Insurance Products with Dependent Claim Frequency and Severity
In this talk, we introduce a novel regression model based on compound distributions for pricing nonlife insurance products with dependent claim frequency and severity. Relaxing the independence assumption in the standard compound distribution, we propose a copula-linked compound distribution that uses a parametric copula to accommodate the association between the frequency and severity components. The resulting copula regression framework is flexible enough to nest several commonly used approaches as special cases, including the hurdle model, the selection model, and the frequency-severity model, among others. We further show that the new model can be easily modified to account for incomplete data due to censoring or truncation. Because of the parametric nature, likelihood-based approaches are proposed for estimation, inference, and diagnostics. In the application, we consider the collective risk model for aggregating losses in an insurance system. Using granular claims data in property insurance, we find substantive negative dependency between the number and the size of insurance claims. We demonstrate that ignoring the frequency-severity association could lead to biased decision-making in insurance operations.