Statistical Models of Claim Distributions in Fire Insurance

Abstract

SummaryThe authors have studied the combined data on claims in fire insurance of dwelling houses reported 1958-1969 by Swedish fire insurance companies The claims were cleared of deductibles and adjusted according to a suitable index Only losses above the largest deductible (in real value) applied during the observation period were included.The material contains four different classes according to the fire resistibillty of the building construction For international comparisons, the pure classes B1 (“stone” dwellings) and B4 (wooden houses) are of interest The distribution of the claims could be well approximated by the log-normal distribution in B1and by the Pareto distribution in B4 An equally good or better fit was obtained by assuming the original loss, reported or not, being distributed according to these distributions and applying the distributions, conditioned by the loss being larger than the deductible in both cases the distribution parameters are functions of the insurance amount in such a way, that the mean value of the loss is described as a power of this amount.The authors refrain from any theoretical arguments for the general applicability of the distributions used They observe, however, the good approximation by wellknown parametric distributions which facilitates many actuarial taks, such as the determination of first loss premiums, deductible premium factors, excess-of-loss premiums etc The agreement between model and reality make these functions fit for use in the models underlying the general risk theory and in the more comprehensive models of the non-life insurance business.