Predictive risk analysis using a collective risk model: Choosing between past frequency and aggregate severity information

The typical risk classification procedure in the insurance field consists of a priori risk classification based on observable risk characteristics and a posteriori risk classification where premiums are adjusted to reflect claim histories. While using the full claim history data is optimal in a posteriori risk classification, some insurance sectors only use partial information to determine the appropriate premium to charge. Examples include auto insurance premiums being calculated based on past claim frequencies, and aggregate severities used to decide workers’ compensation. The motivation is to have a simplified and efficient a posteriori risk classification procedure, customized to the context involved. This study compares the relative efficiency of the two simplified a posteriori risk classifications, that is, those based on frequency and severity. It provides a mathematical framework to assist practitioners in choosing the most appropriate practice.