Modelling dependent data for longevity projections

The risk profile of an insurance company involved in annuity business is heavily affected by the uncertainty in future mortality trends. It is problematic to capture accurately future survival patterns, in particular at retirement ages when the effects of the rectangularization phenomenon and random fluctuations are combined. Another important aspect affecting the projections is related to the so-called cohort-period effect. In particular, the mortality experience of countries in the industrialized world over the course of the twentieth century 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. Also the dependence between ages is an important component in the modeling of mortality (Barrieu et al., 2011). It is observed that the mortality improvements are similar for individuals of contiguous ages (Wills and Sherris, 2008). Moreover, considering the data subdivided by set by single years of age, the correlations between the residuals for adjacent age groups tend to be high (as noted in Denton et al., 2005). This suggests that there is value in exploring the dependence structure, also across time, in other words the inter-period correlation. The aim of this paper is to improve the methodology for forecasting mortality in order to enhance model performance and increase forecasting power by capturing the dependence structure of neighboring observations in the population. To do this, we adapt the methodology for measuring uncertainty in projections in the Lee–Carter context and introduce a tailor-made bootstrap instead of an ordinary bootstrap. The approach is illustrated with an empirical example.