The Asymptotic Efficiency of Largest Claims Reinsurance Treaties

Reinsurance treaties defined as generalizations of the classical largest claims reinsurance covers are investigated with respect to the associated risk, defined as the variance of the insurer’s retaining total claims amount. Instead of the unhandy variance corresponding handier asymptotic expressions are used. With these an asymptotic efficiency measure for comparing two such reinsurance covers is defined. It is shown that with respect to asymptotic efficiency the excess-of-loss treaty is better than the classical largest claims treaty. Furthermore the problem of giving optimal weights to the ordered claims of a generalized largest claims cover is discussed. Reinsurance Research - Pricing/Contract Design