A non-linear mixed model approach for excess of loss benchmark rating

This paper proposes market conform individual benchmark rates for the excess of loss reinsurance of long tail insurance portfolios, that offer market references for the premium rates taking individual contractual conditions into account. The premium rates are expressed in terms of the percentage of the expected premium income of the covered insurance portfolio. We incorporate the specific reinsurance contractual conditions like stabilisation, interest sharing and deposit clauses as well as payment patterns and ’incurred but not (enough) reported’ information. The parameters of the benchmark model are estimated within the framework of non-linear mixed models. This approach allows to correct for different cedent specific conditions in the model, and so we refine the results from Verlaak et al. (Astin Bull 39, 2009) where only one benchmark was proposed for the whole market. The method is applied to the Belgian Motor Third Party Liability XL rates observed from 2001 till 2004.