9 APPLICATIONS OF THE MODEL Using a stochastic model offers additional possibilities for analysing mortality risks. In particular, it is possible to gain insight into the variability on the values of insurance portfolio obligations. As Projections Life Table AG2018 is based on a stochastic model, a statement can be made about the spread of future mortality probabilities around best estimates. The model used not only generates best estimate mortality developments, but can also be used to analyse the uncertainty in future scenarios, based on fluctuations observed in the historical data. It is important to note that the uncertainty intervals presented in this chapter do not take account of parameter or model uncertainty. That is to say, our calculations take the assumed model and the estimated parameters as given fundamentals. Only mortality probabilities are simulated and we assume that we can observe these mortality probabilities exactly. We therefore do not take into account that in practice, working as we do with finite populations, we have at our disposal not the exact mortality probabilities, but only observed ones (the measurement or Poisson noise). In this chapter a number of potential applications of the stochastic model are shown for illustrational purposes. The results listed in this chapter are based on the model portfolios also mentioned in chapter 8, see Appendix B. Firstly, we show in paragraph 9.1 the confidence intervals around the life expectancy produced by the model over the whole horizon. In paragraph 9.2 we discuss the value of the obligations for all potential developments of future mortality probabilities. While the best estimate value of obligations is attained by using best estimate mortality probabilities, we also look at various possible scenarios for mortality probability developments as given by the stochastic model. This provides an insight into the potential increase of the value for the entire portfolio run off at for instance the 95% quantile. In practice, the stochastic distribution of the value of obligations after a one-year shock is also often looked at. To do this, possible shocks during the first year are simulated. Then, for each scenario (shock) the model is recalibrated after adding the new (simulated) observation to the original data set. Based on parameters calibrated per scenario, best estimate mortality probabilities are determined for the remaining years. Paragraph 9.3 shows the confidence intervals this yields for a one-year horizon. Paragraph 9.4 shows the consequences of the resulting stochastic distribution of the value of obligations after a one-year shock and recalibration. Projection Table AG2018 Applications of the model 29
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