A financial analysis of surplus dynamics for deferred life schemes 91Ta b le 1 .Surplus behaviour and related parametersTime E(St) CvaR DS (99%) RoS (99%)
0 1649,899
1 1732,851 179,9519 10.91% − 89 .09%
2 1820,197 362,4452 20.92% − 79 .08%
3 1912,03 556,0326 30.55% − 69 .45%
4 2008,6 727,887 38.07% − 61 .93%
5 2110,173 890,2828 44.32% − 55 .68%
6 2217,03 1051,625 49.84% − 50 .16%
7 2329,47 1211,922 55.66% − 45 .34%
8 2447,811 1333,802 57,26% − 42 ,74%
9 2572,389 1409,132 57.57% − 42 .43%
10 2703,561 1470,693 55.17% − 42 .83%
11 2841,708 1478,472 54.69% − 45 .31%
12 2987,235 1416,793 49.86% − 50 .14%
13 3140,569 1332,953 44.62% − 55 .38%
14 3302,167 1228,486 39.12% − 60 .88%
15 3472,516 1109,346 33.59% − 66 .41%
16 3652,13 982,2259 28.29% − 71 .71%
17 3841,561 840,4843 23.01% − 76 .99%
18 4041,392 660,9939 17.21% − 82 .79%
19 4252,246 443,7866 10.98% − 89 .02%for the whole period of time at a rate which is systematically higher (μ= 4.10% and
r 0 = 3.78%) than the premium rate (2%), thus giving rise to a return on assets always
higher than the average rate of financing. As far as the CVaR is concerned, it shows a
dynamic which is totally consistent with the mathematical provision time evolution, as
one can expect as has already been shown elsewhere [3], the financial risk dynamic is
mainly driven by the mathematical provision time progression. Accordingly, the time
evolution of the RoS, as defined in Section 2, is directly influenced by the mathematical
provision and its absolute value, as can easily be seen, is dependent on the confidence
level chosen. As far as the connection with the reserve dynamic is concerned, we
can state that both DS and worst expected RoE prove to be fully consistent with the
traditional and pragmatic idea that the lower the reserve the higher the risk of the
business. Therefore, distributable earnings can be quantified and managed, through
this approach, in order to minimise the ruin probability on the basis of both the general
investment strategy and the specific market condition available at time of issue.
5 Conclusions and future research prospect
The sketched model proves to be a way to quantify the amount of distributable earnings
year-by-year with reference to a specific portfolio of policies as it gives the oppor-
tunity to build upon a complete distribution budget. Since we concentrate solely on