Giuseppe Melisi

The variability of claim costs represents an important risk component, which should be taken into account while implementing the internal models for solvency evaluation of an insurance undertaking. This component can generate differences between future payments for claims and the provisions set aside for the same claims (run-off error).
If the liability concerning the claims reserve is evaluated using synthetic methods, then the run-off error depends on the statistical method adopted; when it is not possible to study analytically the properties of the estimators, methods based on stochastic simulation are particularly effective. This work focuses on measuring the run-off error with reference to claims reserves evaluation methods applied to simulated run-off matrices for the claims settlement development. The results from the numerical implementations provide the authors with useful insights for a rational selection of the statistical-actuarial method for the claims reserve evaluation on an integrated risk management framework.
The setting of the analysis is similar to that adopted in other studies (Stanard, 1986; Pentikainen and Rantala, 1992; Buhlmann et al., 1980), however, it differs for estimation and simulation methods considered and for the statistics elaborated in the comparison.

Keywords: run-off error, outstanding claims reserves, stochastic simulation

Loss portfolio transfer (LPT) is a reinsurance treaty in which an insurer cedes the policies that have already incurred losses to a reinsurer. This operation can be carried out by an insurance company in order to reduce reserving risk and consequently reduce its capital requirement calculated, according to Solvency II. From the viewpoint of the reinsurance company, being a very complex operation, importance must be given to the methodology used to determine the price of the treaty.
Following the collective risk approach, the paper examines the risk profiles and the reinsurance pricing of LPT treaties, taking into account the insurance capital requirements established by European law. For this purpose, it is essential to calculate the capital need for the risk deriving from the LPT transaction. In the case analyzed, this requirement is calculated under Solvency II legislation, considering the measure of variability determined via simulation. This quantification was also carried out for different levels of the cost of capital rate, providing a range of possible loadings to be applied to the premium.
In the case of the Cost of Capital (CoC) approach, the results obtained provide a lower level of premium compared to the percentile-based method with a range between 2.69% and 1.88%. Besides, the CoC approach also provides the advantage of having an explicit parameter, the CoC rate whose specific level can be chosen by the reinsurance company based on the risk appetite.