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Computational framework for longevity risk management
Longevity risk threatens the financial stability of private and government sponsored defined benefit pension systems as well as social security schemes, in an environment already characterized by persistent low interest rates and heightened financial uncertainty. The mortality experience of countries in the industrialized world would suggest a substantial age-time interaction, with the two dominant trends affecting different age groups at different times. From a statistical point of view, this indicates a dependence structure. It is observed that mortality improvements are similar for individuals of contiguous ages (Wills and Sherris, Integrating financial and demographic longevity risk models: an Australian model for financial applications, Discussion Paper PI-0817, 2008). Moreover, considering the dataset by single ages, the correlations between the residuals for adjacent age groups tend to be high (as noted in Denton et al., J Population Econ 18:203-227, 2005). This suggests that there is value in exploring the dependence structure, also across time, in other words the inter-period correlation. In this research, we focus on the projections of mortality rates, contravening the most commonly encountered dependence property which is the "lack of dependence" (Denuit et al., Actuarial theory for dependent risks: measures. Orders and models, Wiley, New York, 2005). By taking into account the presence of dependence across age and time which leads to systematic over-estimation or under-estimation of uncertainty in the estimates (Liu and Braun, J Probability Stat, 813583:15, 2010), the paper analyzes a tailor-made bootstrap methodology for capturing the spatial dependence in deriving confidence intervals for mortality projection rates. We propose a method which leads to a prudent measure of longevity risk, avoiding the structural incompleteness of the ordinary simulation bootstrap methodology which involves the assumption of independence
Bayesian probabilistic projections of life expectancy for all countries
We propose a Bayesian hierarchical model for producing probabilistic forecasts of male period life expectancy at birth for all the countries of the world to 2100. Such forecasts would be an input to the production of probabilistic population projections for all countries, which is currently being considered by the United Nations. To evaluate the method, we conducted an out-of-sample cross-validation experiment, fitting the model to the data from 1950-1995 and using the estimated model to forecast for the subsequent 10 years. The 10-year predictions had a mean absolute error of about 1 year, about 40 % less than the current UN methodology. The probabilistic forecasts were calibrated in the sense that, for example, the 80 % prediction intervals contained the truth about 80 % of the time. We illustrate our method with results from Madagascar (a typical country with steadily improving life expectancy), Latvia (a country that has had a mortality crisis), and Japan (a leading country). We also show aggregated results for South Asia, a region with eight countries. Free, publicly available R software packages called bayesLife and bayesDem are available to implement the method