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Typical risk classification procedure in insurance is consists of a prioririsk classification determined by observable risk characteristics, and aposteriori risk classification where the premium is adjusted to reflect thepolicyholder's claim history. While using the full claim history data isoptimal in a posteriori risk classification procedure, i.e. giving premiumestimators with the minimal variances, some insurance sectors, however, onlyuse partial information of the claim history for determining the appropriatepremium to charge. Classical examples include that auto insurances premium aredetermined by the claim frequency data and workers' compensation insurances arebased on the aggregate severity. The motivation for such practice is to have asimplified and efficient posteriori risk classification procedure which iscustomized to the involved insurance policy. This paper compares the relativeefficiency of the two simplified posteriori risk classifications, i.e. based onfrequency versus severity, and provides the mathematical framework to assistpractitioners in choosing the most appropriate practice.

Predictive Risk Analysis in Collective Risk Model: Choices between Historical Frequency and Aggregate Severity