Measuring mortality heterogeneity in pension annuities

Pension plan sponsors face a myriad of risks, one of which is longevity risk that arises from the increasing life expectancy trends among pensioners. Traditionally, plan sponsors manage longevity risk by forecasting the mortality rates. However, recent acceleration in longevity improvement forces the insurance companies to assess accurately the survival trend, in order to avoid paying much longer than expected. As regards the mortality trend we have to empathize different features with respect to mortality due to different race, ethnicity, income, wealth, marital status, educational attainment and so on. The mortality heterogeneity tends to determine a phenomenon termed as overdispersion, according to which the variance compared to the mean increases. Some authors take into account the mortality overdispersion by estimating the parameter in a mixed Poisson model. In the current literature, there are several papers which have considered the modelling and forecasting of population mortality using the Lee-Carter framework. In this paper, we propose an extended version of the model under consideration, in order to capture the phenomenon of the heterogeneity in mortality trend, by using the geographical stratification of the population. Diagnostic plots are provided to show the results and actuarial application is performed in a context of pension products.