Mathematical and Statistical Methods for Actuarial Sciences and Finance

182 S. Levantesi and M. Menzietti

Ta b le 8. Present value of future profits as ratio to total single premium income,
Y( 0 ,T)/( ( 0 ,ω)N 1 ( 0 ))with initial capitalK( 0 )=RBC 99 .5%( 0 , 1 )

SL = 10% SL = 20% %

To ta l 6 .21% 11 .85% 91%

Insurance 3 .03% 6 .17% 104%

Patrimonial 3 .18% 5 .69% 79%

sources separately, we have a higher increase inYI( 0 ,T)than inYP( 0 ,T): 104%
compared to 79%.

7 Conclusions

This paper focuses on disability and longevity risks arising from issues in the estimate
of residual life expectancy of healthy and disabled people. Our analysis highlights
that the EPs are affected by a significant demographic risk caused by systematic
deviations between expected and realised demographic scenarios. The results confirm
that such a risk is difficult to control, depending on uncertainty in the future evolution
of biometric functions. The risk reserve distribution shows a strong variability due to
the demographic scenario changes affecting the technical provision valuation. Since
such a risk is systematic, theu(t)variability does not lessen when either safety loading
or initial capital increase. Nonetheless, they are useful tools in managing demographic
risk because they significantly reduce the ruin probability of the insurance company
as far as the RBC requirements necessary to ensure the insurer solvency at a fixed
confidence level. In this paper we take intoaccount an initial capital only, reducing the
probability of incurring losses. However, the risk of systematic deviations persists,
requiring an appropriate capital allocation strategy. This topic will be the subject of
future research together with a suitable reinsurance strategy.

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