Risk Factor Contributions and Capital Allocation in Life Insurance in the Solvency II Framework

A life insurance company with a portfolio composed either by annuities or by term insurance contracts is considered. It is well known that such portfolios are exposed to different risk sources, but interest rates risk and mortality risk are the main ones. On the one hand, interest rates affect the value of the bonds in which the asset portfolio is usually invested, and on the other hand, they are used to determine the discounting factor in liabilities evaluation. Mortality rates influence the benefit amount paid to the policyholders. The total portfolio loss is nonlinear with respect to risk factors. Our aim is to examine the contributions of the investment risk factor and the insurance risk factor to the future liability values under different allocation methods.