7 UNCERTAINTY The projection model presented in this publication is based on mortality data from the past. Trends observed in the historical data are extended into the future in the best possible way. The future being uncertain, the values that will be found for the actual mortality rates in the Netherlands will deviate from the best possible estimations at this moment in time. AG elects to explicitly chart this uncertainty too. The model equations in Appendix A invite users to not only apply a fixed projections table. Actuaries can use them to generate stochastic scenarios by simulation. That yields a collection of possible future mortality probability scenarios, similar to scenarios produced for future interest rate curves and investment yields. There are other forms of uncertainty as well. The parameters in the projection model are estimated from observed deaths, which constitute a limited sample. That implies that there is also uncertainty in the projection model’s estimated parameters. Below, besides this ‘parameter risk’, we also discuss the uncertainty about the validity of the chosen model, the so-called ‘model risk’. 7.1 Parameter uncertainty We assume that the number of deaths follows a Poisson distribution with a mean depending on the modelled trend. The observed numbers of deaths constitute a sample from that distribution. This raises the question what the effect on the estimated parameters is of the limited sample size. Through Eurostat, the HMD and CBS we possess reliable data on the numbers of deaths in the past. As the parameters are based on a multitude of observations over multiple years from both The Netherlands and the rest of Europe, the estimation is far less uncertain than if only a smaller population would have been used. Nonetheless, it is advisable to analyse the effect of using a sample. The statistical method that can be used for this, the bootstrap, is based on a so-called resampling technique. In this method, myriad possible numbers of deaths are simulated for a given set of parameters from the corresponding Poisson distribution. For each of these samples the parameters are recorded that would be found if that sample had been used to calibrate the model. This provides an insight into the uncertainty of the parameter values found. If roughly the same parameter values are found in each of the possible samples, the effect of the sample on the parameters is small. If, on the other hand, a large variation shows in the parameter values generated in this way, then parameter uncertainty is large. Table 7.1 shows the results of the bootstrap procedure for 10,000 AG2018 model samples. For all parameters the 2.5%, 25%, 50%, 75% and 97.5% quantiles are given. Projection Table AG2018 Uncertainty 19
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