Nicolino Ettore D’Ortona

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

In the context of the stochastic models for the management of life insurance portfolio, the authors explore, with simulation approach, the effects induced by the application of a particular method of calculation of the surrender value.
In the life insurance, the policyholder position is, at any moment, quantified by the mathematical reserve. In case the reserve amount results are positive, the insurance company can allow the contract surrender, consisting in an amount payment, called surrender value, commensurate with the mathematical reserve.
Generally, the insurance company enforces some restrictions in the surrender value determination, in order to avoid, first of all, that an amount is disbursed to the policyholder while, on the contrary, he results to be indebted to the Company. In this paper the authors will consider a surrender value calculation method based precisely on the profit recovery concept which shall be supplied by the contract in case it remains in the portfolio. Additionally, the authors shall analyze, by simulation approach, the effects caused by the enforcement of the surrender value calculation concept on a life portfolio profitability, and on the penalties extent enforced to the policyholders which cancel from the contract.

Keywords: surrender value, life insurance, internal risk model, 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.