Safety loading in the annuity pension fund dynamics

The portfolio consistency fund studied in the paper is referred to a pension scheme of beneficiaries entering in the retirement state at the same time. It arises from the payment stream consisting in cash flows due at the beginning of each year in case of life of the pensioner: in the deferment period, in the form of premiums entering in the fund, and during the retirement period, in the form of instalments getting out of it. The fund dynamic as function of the time of valuation evolves increasing thanks to the interest maturing on the accumulated fund and decreasing because of the benefits paid to the survivals. Both the mortality trend, determining the number of payments at each time, and the interest maturing on the fund, are considered deterministically unknown at the moment of the contract issue. Stochastic assumptions about the behaviour of the interest rate process and the description of the mortality trend betterment, most likely to be expected in very long periods and in civilized world, provide a dynamic description of the pension scheme and in particular of the pension fund. In the paper we want to deepen the aspect of the financial and demographic basis chosen for premium calculation with respect to the impact on the portfolio fund consistency and on the risk arising from the randomness in the choice of the survival model used for the valuations. To this aim, we will assume for the fund description different projection levels for the survival probabilities and the Vasicek hypotheses for the interest rates maturing on the fund itself; moreover, we will determine the premium amounts introducing different scenarios in a safety loading perspective. As evident, in the premium quantification lower interest rate jointly with higher survival probabilities constitute a form of implied loading. The numerical application presented in the paper shows how the change in the premium calculation conditions affects the portfolio fund consistency in the different scenarios and investigates on the impact they have on the Demographic Model Risk Measure. Useful information for managing aim can be derived. © 2009 IOS Press. All rights reserved.