A Note On The Multiplicative Ratemaking Model

Abstract

The multiplicative ratemaking, model we have in mind is the following one. Within a certain branch of insurance we have, say for simplicity, two tarif arguments U and V. For example, in motor insurance we could think of U and V as being make of car and geographical district respectively. In fire insurance U could be class of construction for buildings and V could relate to fire defense capacities.The arguments are of a qualitative nature and argument U has r levels, while argument V has k levels. To our disposal we have statistical experience of the business for a certain period of time, consisting of—risk exposures nij (i = 1 … r, j = 1 … k).Risk exposure nij thus corresponds to the ith U-level and the jth V-level. It could be e.g. number of policy years or sum insured during the period of observation for objects belonging simultaneously to U-level i and V-level j.The nijS are known non-random quantities.—(relative) risk measures pij(i = 1 … r, j = 1 …k).Risk measure pij could be e.g. claims frequency, i.e. number of Claims divided by number of policy years, or claims cost per policy year or claims cost as a percentage of sum insured. In general pij is thus the observed number or the observed amount of claims belonging simultaneously to U-level i and V-level j, divided by the corresponding risk exposure nij.