Insurance: Mathematics and Economics 27 2000 285–312
An investigation into parametric models for mortality projections, with applications to immediate annuitants’
and life office pensioners’ data
Terry Z. Sithole, Steven Haberman, Richard J. Verrall
∗
Department of Actuarial Science and Statistics, City University, Northampton Square, London EC1V 0HB, UK Received 1 December 1999; received in revised form 1 May 2000; accepted 30 June 2000
Abstract
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. © 2000 Elsevier Science B.V. All rights reserved.
Keywords: Mortality projections; Immediate annuitants; Life office pensioners
1. Introduction
Mortality has shown a gradual decline over time, with the rates of decline not being necessarily uniform across the age range. For pensioners and annuitants, it is important to be able to accurately measure changes in mortality over
time since the policyholders’ benefits depend on survival. If the standard mortality table used to calculate annuity rates and reserves predicts higher mortality rates than actually experienced by the policyholders, the policyholders
will have been undercharged, and the company will incur losses. Also reserves will be understated.
In UK, the Continuous Mortality Investigations CMI committee of the Institute and Faculty of Actuaries makes projections of future improvements in the mortality of pensioners and annuitants. The procedure essentially involves
two stages. Firstly, for a given investigation period, the data are graduated and mortality tables produced. In the second stage, projected mortality tables are produced by applying reduction factors derived from a consideration of
past improvements and likely future improvements in the mortality rates.
∗
Corresponding author. E-mail address: r.j.verrallcity.ac.uk R.J. Verrall.
0167-668700 – see front matter © 2000 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 7 - 6 6 8 7 0 0 0 0 0 5 4 - 8
286 T.Z. Sithole et al. Insurance: Mathematics and Economics 27 2000 285–312
Renshaw et al. 1996 suggested a modelling structure in the framework of generalised linear models, which incorporates both the age variation in mortality and the underlying trends in the mortality rates. In this paper, we
use this modelling structure to investigate mortality trends for immediate annuitants and life office pensioners. We focus on the projected forces of mortality and mortality improvement factors derived from the appropriate model
for each experience.
Section 2 covers the current practice of the CMI in projecting mortality rates. In Section 3, the modelling structure suggested by Renshaw et al. 1996 is given. The application of the structure in modelling immediate annuitants’
and pensioners’ mortality experiences is discussed in Section 4, while in Section 5 we give a brief outline of a procedure for modelling select mortality and how this can be applied to the annuitants’ select data.
2. Current CMI practice in projecting mortality
