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 n ij ( i = 1 … r , j = 1 … k ). Risk exposure n ij thus corresponds to the i th U -level and the j th 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 n ij S are known non-random quantities. —(relative) risk measures p ij ( i = 1 … r , j = 1 … k ). Risk measure p ij 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 p ij 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 n ij .