Life office management perspectives by actuarial risk indexes

The study focuses on the quantitative risk analysis of a pension scheme referred to a portfolio of beneficiaries entering in the retirement state at the same time. The structure of the cash flow consists in constant payments due at the beginning of each year in case of life of the pensioner. In particular, the paper concerns the financial periodic portfolio funds arising from the payment stream with the aim to investigate the capability of the funded premium payments made in the deferment period of fronting the future obligations. We consider the two flows in and out of the portfolio as forces operating in opposite directions, the first consisting in the increasing effect due to the interest maturing on the accumulated fund, the second in the outflow represented by the benefit payments to the survival. The two processes are compared in a scenario in which the financial risk and the demographic risk are considered. Posing the time of valuation coinciding with the contract entry time, we consider deterministically unknown the dynamic of the future behaviour of both the interest rates maturing on the fund and of the mortality. The mortality trend betterment in very long periods, as in the pension cases happens, leads to the need of a careful consideration of the systematic deviations of the number of deaths from the expected values. As known, if the risk arising from the accidental deviations of mortality can be hedged by pooling strategies, such that it is possible to neglect this risk source in the case of sufficiently large portfolios, the risk arising from the longevity phenomenon cannot be avoided without making dangerous mistakes of underestimation of future obligations. The scenario in which the study is framed consists in stochastic hypotheses on the evolution in time of the interest rates of return on investment of the fund and in a more complex description of the mortality trend. The aim of the paper is, in particular, to study the consequences on the portfolio fund values, of the change in the mortality description. The survival forecasting made at the time of the contract issue, even if considered with a certain degree of projection, isn't likely to be the same we can forecast, for example, at the time of the retirement age. The choice of the “right” mortality table means the choice of the “right” projection level to attribute to the mortality trend. Risk filters and opportune indexes are considered and illustrated.