A Statistical Perspective on Actuarial Methods for Estimating Pure Premiums from Cross-Classified Data

Traditional actuarial methods for predicting pure premiums on the basis of cross-classified data can be regarded as statistical estimates of model parameters. This article develops a simplified model of claim generation and uses it to illuminate the properties of various proposed cross-classification methods. Although traditional methods have natural interpretations in statistical terms, they do not utilize the data in a fully efficient way. By developing more realistic models and applying more sophisticated statistical techniques, it may be possible to improve substantially the accuracy of pure premium prediction.