Ratings of Largest Claims and Econo-Reinsurance Treaties for Large Portfolios

In the present paper we deal with the problem of calculating a premium for the largest claims and ECOMOR reinsurance treaties. AMMETER derived already In 1964 formulas for calculating the premiums of the largest claims and ECOMOR reinsurance treaties (compare also SEAL (1969), TH~PAUT (1950)), which we will restate in the following Section 2. Lately BENKTANDER (1978) has established an interesting connection between the premiums of the largest claims and excess of loss reinsurance treaties. He proved that the net risk premium of the largest claims treaty covering the p largest claims is bounded by the risk premium of an excess of loss treaty plus p times its priority, which has to be determined such that the mean number of excess claims equals p. Furthermore Benktander showed in examples that the upper bound is quite good in case of the Poisson-Pareto risk process. Nevertheless he did not give a formal proof for the quality of the bound m the Poisson-Pareto case nor for other risk processes.