Safety loading in the annuity pension fund dynamics

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 analysis starts from the retirement time of the contractors and concerns the dynamic behaviour of the financial periodic portfolio fund cut down year by year by the payments due to the survivals. 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 survival forecasting made at the time of the contract issue, even if considered with a certain degree of projection, is not likely to be the same we can forecast. The choice of the “right” mortality table means the choice of the “right” projection level to attribute to the mortality trend. The aim of the paper is to study in particular the impact of the change in the mortality description on the portfolio fund values. Risk filters and opportune indexes are considered and their behaviour illustrated.