Risk measures in solvency regulation: reinsurance layers and unexpected loss

Abstract

The total amount of damage to be paid by an insurance company can be represented as the sum of (reinsurance-)layers, some of which may be transferred to a reinsurer on the basis of an excess of loss treaty. Some risk measures associated with the layers are here investigated, by paying particular attention to the Unexpected Loss function which plays a role in the Solvency II legislative program: in fact in non-life insurance, the standard formula for the calculation of premium and the reserve capital requirement are mainly based on its definition. Starting from the assumption of discrete random variables, explicit formulas and ranges of variation are derived that are useful for its approximate evaluation.Mathematics Subject Classification: 62P05