Bayesian Models for Computer-Aided Underwriting

Bayesian models for computer-aided underwriting have been developed for a major composite insurance company for two classes of commercial business: motor fleet and fire. The fire model produces a posterior probability distribution over a discretized dimension of risk, defined as the probability of a loss times the severity of the loss, but operationalized as a rate appropriate for that degree of risk. A separate model is developed for each class of risk (e.g. shops, warehouses). In its generic form, the fire model comprises 10-13 factors (e.g. housekeeping, security) and three possible levels for each factor (e.g. for housekeeping, untidy, average, tidy). A branch underwriter using the model identifies the factor levels appropriate to the building under consideration; the computer then selects the corresponding pre-assessed likelihoods, computes posterior probabilities and expected rates, and displays the rate along with a credibility factor that indicates the relative plausibility of this pattern of factor levels. The models have been tested on over 500 actual risks presented to branch underwriters, and the pure rates generated by the model were found to be at least as good as rates determined for the same risks by experienced underwriters. The motor fleet model gives the predictive distribution of the total claims cost for a fleet. Frequency and size of claims are assumed to be described by a compound Poisson model with parameters that are modified by three to five years' claims experience of the fleet relative to the experience of the whole portfolio of fleets, by the nature of the business carried out by the vehicles in the fleet and by the geographical district in which the fleet usually resides. This model has been tested on over 300 cases drawn from the files and has generated rates considered by head office underwriters to be satisfactory. Both models, which can easily be implemented on microcomputers, demonstrate how the Bayesian approach provides a general and flexible framework within which both hard data and expert judgement can be accommodated. In this sense, these models are among the first in a new generation of underwriting models that extend the capabilities of underwriters.