The Cox Regression Model for Claims Data m Non-Life Insurance

The Cox regression model is a standard tool in survival analysis for studying the dependence of a hazard rate on covariates (parametrically) and time (nonparametrically). This paper is a case study intended to indicate possible applications to non-life insurance, particularly occurrence of claims and rating. We studied individuals from one Danish county holding policies in auto, property and household insurance simultaneously at some point during the four year period 1988-1991 in one company. The hazard of occurrence of claims of each type was studied as function of calendar time, time since the last claim of each type, age of policy holder, urbanization and detailed type of insurance. Particular emphasis was given to the technical advantages and disadvantages (particularly the complicated censoring patterns) of considering the nonparametrically underlying time as either calendar time or time since last claim. In the former case the theory is settled, but the results are somewhat complicated. The latter choice leads to several issues still under active methodological development. We develop a goodness-of-fit criterion which shows the lack of fit of some models, for which the practical conclusions might otherwise have been useful.