Estimation of General Rating Models for Insurance

In general insurance tariffs consist of two components: First risks are classified according to a vector of basic criteria, say Xt, which for example in automobile insurance depend on the type or the power of the vehicles. Given the basic premiums, Xta, further extra charges and discounts are rated depending on usually more individual characteristics of the risk (say Zt). All relevant tariffs can be represented by a Generalized Rating Model that determine the net expected premium by E(yt) = Xta.exp{Ztb} While previous work focused either the estimation of linear (Xta) or multiplicative models (exp{Ztb}), we will estimate the parameters of the two linear kernel functions simultaneous by Maximum-Likelihood methods. This allows a valid selection and testing of rating criteria within the market-relevant tariff structure without misleading evidence due to divergent modelstructures. The efficiency of the suggested tariff can immediately be judged by ML-statistics and information criteria. We illustrate the model and the estimation with examples from the Austrian motor liability market. Restricted net-tariff estimations provide premium structures which are consistent with exogenous fixed components like a Bonus-Malus scale or traditionally applied discounts.