Largest Claims Reinsurance (LCR). A Quick Method to Calculate LCR-Risk Rates from Excess of Loss Risk Rates

Abstract

Let us denote by E(x) the pure risk premium of an unlimited excess cover with the retention x and by H(x) and m(x) the corresponding expected frequency and severity. We thus have E(x) = H(x) · m(x) . H(x) is a non-increasing function of x and for practical purposes we can assume that it is decreasing; H ′( x ) < o. The equation H(x) = n has then only one solution x n , where n is a fixed integer. Let E n denote the risk premium for a reinsurance covering the n largest claims from the bottom. Let us define Intuitively we feel that is a good approximation for E n . We shall first show that when the claims size distribution is Pareto and the number of claims is Poisson distributed, is a good approximation for E n , being slightly on the safe side. We further include a proof given by G. Ottaviani that the inequality always holds. In the Pareto case we have where the Poisson parameter t stands for the expected number of claims in excess of 1 (equal to a suitably chosen monetary unit) and .