120 V. D’Amato and M. Russolillo
Fig. 5.Portfolio of 1000 pension annuities,x=45,t=20,r=100. Fixed rate at 3%description, in the light of the main results of [2]. In the following graphs (see Figs. 5
and 6) we represent the portfolio funds along with the potential whole contract life, i.e.,
both into theaccumulation phaseand into theannuitisation phase. The portfolio funds
trend is calculated on a pension annuity portfolio referred to a cohort ofc= 1000
beneficiaries agedx=45 at timet=0 and entering in the retirement state 20 years
later, that is at age 65. The cash flows are represented by the constant premiumsP,
payable at the beginning of each year up tot=20 in case the beneficiary is still alive
at that moment (accumulation phase) and by the constant benefitsR=100 payable at
the beginning of each year aftert=20 (annuitisation phase) in case the beneficiary
is still alive at that moment. Figure 5 shows how the portfolio funds increase with
Fig. 6.Portfolio of 1000 pension annuities,x=45,t=20,r=100. Stochastic rate of return