Excess frequency fitting for long tailed risks

Speaker: Markus Knecht
It is widespread practice in short tailed lines to model the large loss activity by fitting a distribution to the empirical samples available. This method does not extend in a straight forward manner to long tailed lines as the empirical data available are still developing. Often some single loss development methods are used to be able fit to the ultimates.
We propose an alternative and practical method based on excess frequency estimators rather than empirical ultimate losses that has been successfully implemented by several reinsurances for pricing excess of loss liability treaties.
Combining automated excess frequency triangle developments at various levels with secondary uncertainties estimators on the ultimate projections allows a curve fitting in a similar way than in the short tail case.The method is simple, more robust than single loss development approaches for smaller loss sets and robust against trend - like superimposed inflation - and pattern varying by excess points making it a suitable candidate for modelling high excess liability programs.