A Combination of Surplus and Excess Reinsurance of a Fire Portfolio

Reinsurance forms can roughly be classified into proportional and non-proportional. The authors of this paper had planned to investigate the “efficiency†of two different reinsurance forms, one from each of these categories. Efficiency is here understood as reduction in the variance of the annual results of the risk business achieved per unit of ceded reinsurance risk premium. This investigation may be carried out in full later.This note will only deal with the interplay between surplus and excess of loss reinsurance; more specifically the effect of changes in the volume of surplus cessions on the excess of loss risk premium.The study came out of a practical Fire Reinsurance rating problem and will be carried through under very simplified assumptions. Thus we will ignore the conflagration hazard and the possibility of a wrongly taxed PML. This means that if amounts above a PML of M are ceded on a surplus basis the highest loss per event will be M, and an excess cover above a priority m will never pay more than M-m per event.The following notations will be usedR(M) ceded risk premium volume on surplus basis, the PML retention being M.πM(m) excess of loss risk premium if priority is m and surplus cessions are made above a PML of M.