Dependent frequency–severity modeling of insurance claims

Standard ratemaking techniques in non-life insurance assume independence between the number and size of claims. Relaxing the independence assumption, this article explores methods that allow for the correlation among frequency and severity components for micro-level insurance data. To introduce granular dependence, we rely on a hurdle modeling framework where the hurdle component concerns the occurrence of claims and the conditional component looks into the number and size of claims given occurrence. We propose two strategies to correlate the number of claims and the average claim size in the conditional component. The first is based on conditional probability decomposition and treats the number of claims as a covariate in the regression model for the average claim size, the second employed a mixed copula approach to formulate the joint distribution of the number and size of claims. We perform a simulation study to evaluate the performance of the two approaches and then demonstrate their application using a U.S. auto insurance dataset. The hold-out sample validation shows that the proposed model is superior to the industry benchmarks including the Tweedie and the two-part generalized linear models.