An investigation into parametric models for mortality projections, with applications to immediate annuitants’ and life office pensioners’ data

This paper investigates the use of parametric models for projecting mortality rates. The basic framework used is that of generalised linear and non-linear models and can be considered as an extension of the Gompertz–Makeham models [Forfar et al., J. Inst. Actuaries 115 (1988) 1; Trans. Faculty Actuaries 41 (1988) 97] to include calendar period. The data considered are the CMI ultimate experience for immediate annuitants (male and female) over the period 1958–1994, and for life office pensioners (male and female) over the period 1983–1996. The modelling structure suggested by Renshaw et al. [British Actuarial J. 2 (II) (1996) 449] is used to investigate the data sets pertaining to the ultimate experiences, and to determine a range of suitable models, analysing the data by age and calendar period. The properties of these models are investigated and recommendations are made on which models are appropriate for use in projections. The select experience for immediate annuitants’ is modelled using the structure suggested by Renshaw and Haberman [Insurance: Math. Econ. 19 (2) (1997) 105]. Projected forces of mortality using the recommended model are given for each experience. These are compared with the CMI projected mortality rates.