9 APPLICATIONS OF THE MODEL The use of a stochastic model offers opportunities in relation to the analysis of mortality risks. In particular, it is possible to obtain an insight into the variability of the value of the liabilities of insurance portfolios. Since the Projection Table AG2016 is based on a stochastic model, it is possible to draw conclusions on the spread of future mortality probabilities around the best estimate. In essence, the model used extrapolates not only mortality developments, but also the variability (volatility) of these. This volatility is consequently representative of uncertainty, such as occurred in the past. It is important to note that the uncertainty intervals presented in this publication do not take into account uncertainty in relation to parameters or the model. In other words, these intervals take the assumed model and the estimated parameters as the point of departure. In this chapter, several possible applications of the stochastic model are mentioned by way of illustration. The results stated in this chapter are based on the same model portfolios as those referred to in chapter 8. In the first application, we consider the value of the liabilities for all possible developments of future mortality probabilities. Where the best estimate value of the liabilities can be estimated by using the best-estimate mortality probabilities, we have considered the possible development in mortality probabilities on the basis of the likelihood that they will occur, as shown by the stochastic model. This gives an insight into the possible increase in the total run-off of liabilities, for instance, in the 95% quantile. A second application relates to the stochastic distribution of the best-estimate portfolio value, based on an horizon of 1 year. In this regard, consideration is only given to possible shocks during the first year and the best estimate is subsequently used. In other words, shocks in subsequent years are set at nil. This application shows what can happen in a year and the increase in the liabilities which results from this. Finally, we show a third application in which the stochastic model is used to determine confidence intervals in relation to life expectancy. In case of the above applications, no conclusions are drawn with regard to the consequences for the calculation of the buffers created in accordance with Solvency II. Basing the amount of capital to be tied up for mortality risk exclusively on the distribution resulting from the stochastic model could result in underestimating the required capital. The stochastic model, after all, does not take into account parameter uncertainty, nor model uncertainty. Projection Table AG2016 Applications of the model 26
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