Past mortality experience has shown that the variability in mortality levels is not constant and can be higher than what the usual Poisson assumption implies. This paper proposes two ways to tackle the heterogeneity often present in mortality data. First, an additional dispersion submodel is developed and combined with the mean model to perform a joint modelling of the mean and the dispersion. Moreover, a flexible group of distributions called the Tweedie family is adopted to model the number of deaths. Using Australian and other mortality data, the results of this study show that this Tweedie double modelling framework can generally improve the fitting performance and also leads to a more adequate allowance for longevity risk when valuing pension annuities.
- Dispersion modelling
- double generalised linear model
- Tweedie distributions
- common factor model