Predicting Automobile Insurance Claim Rate Versus Through Severity and Frequency Predictions

We consider a Regression problem in which the Target is a function of two or more variables. One can either predict the target value directly or predict the component variables and then compute the Target value. A common example is automobile insurance claims. One can compute Frequency and Severity separately and then take the product to determine the amount claimed per year (which we call the Total Claim Severity or Claim Rate) or one may compute the claims paid per year for each customer and then predict this value directly. We show that theoretically, the performance is better if one predicts the computed value (e.g., Total Claim Severity) directly rather than predicting the individual components (e.g., frequency and severity) and then calculating the Total Claim Severity as the product. We illustrate the differences experimentally using data for customers from a real insurance company.