Exposure-Rating in Liability Reinsurance

The well-known inflation-independent exposure rating curves from Property reinsurance (see e.g. Mack (1980) or Bernegger (1997)) cannot be deduced in Liability insurance in the same way because here the claims sizes cannot be assumed to be scaled by the sums insured. Instead, German insurance and reinsurance companies apply a specific system of increased limits factors introduced already in 1936 by the pioneer of German non-life insurance mathematics, Paul Riebesell. In the paper, Riebesell’s system is analysed in the light of the Collective Model of Risk Theory. It is shown that Riebesell’s system is consistent with the Collective Model only above some threshold u>0 and under the assumption that there the claims sizes have a Pareto distribution F(x) =1- (x/c)-a with parameters c