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), Thépaut (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 in the Poisson-Pareto case nor for other risk processes.

In the following note we take up this last point and prove that for general risk process Benktander's upper bound is equivalent to the premium of the largest claims reinsurance cover when the size of the collective approaches infinity. Consequently, for large portfolios the risk premium of the largest claims cover may be replaced by the upper bound, e.i., calculated from the premium of the corresponding excess of loss treaty. Moreover we state a similar result for the ECOMOR treaty.