**DISCUSSION PAPER PI-0801**

Mortality Density Forecasts: An Analysis of Six Stochastic Mortality Models

Andrew J. G. Cairns, David Blake, Kevin Dowd, Guy D. Coughlan, David Epstein, and Marwa Khalaf-Allah

We investigate the uncertainty of forecasts of future mortality generated by a number

of previously proposed stochastic mortality models. We specify fully the stochastic

structure of the models to enable them to generate forecasts. Mortality fan charts

are then used to compare and contrast the models, with the conclusion that model

risk can be significant.

The models are also assessed individually with reference to three criteria that focus

on the plausibility of their forecasts: biological reasonableness of forecast mortal-

ity term structures; biological reasonableness of individual stochastic components of

the forecasting model (for example, the cohort e®ect); and reasonableness of forecast

levels of uncertainty relative to historical levels of uncertainty. In addition, we con-

sider a fourth assessment criterion dealing with the robustness of forecasts relative

to the sample period used to ¯t the model.

To illustrate the assessment methodology, we analyse a data set consisting of national

population data for England & Wales, for Males aged between 60 and 90 years

old. We note that this particular data set may favour those models designed for

application to older ages, such as variants of Cairns-Blake-Dowd, and emphasise

that a similar analysis should be conducted for the specific data set of interest to

the reader. We draw some conclusions based on the analysis and compare to the

application of the models for the same age group and gender for the United States

population. Finally, we note the broader application of the approach to model

selection for alternate data sets and populations.

Keywords: Stochastic mortality model, cohort erect, fan charts, model risk, fore-

casting, model selection criteria.

**DISCUSSION PAPER PI-0605**

**The Impact of Occupation and Gender on Pensions from Defined Contribution Plans**

*David Blake, Andrew Cairns and Kevin Dowd*

We present simulation results for the likely pension outcomes (measured in terms of the distribution of the pension ratio of actual pension to some fraction of final salary) for different defined contribution pension plan members distinguished by occupation and gender. Whilst our results suggest that key differences between outcomes depend on the strategic asset allocation strategy chosen (and hence on the rate of return on assets in relation to the growth rate in earnings), we also find that DC plans benefit most those workers who have the highest career average salary relative to final salary or whose salary peaks earliest in their careers. Thus low-skilled workers and women do relatively well from DC plans: the largest pension difference between occupations is 34% (for men) and 38% (for women), while the largest pension difference between women and men in the same occupation is 45%. We conclude that key aspects of plan design (in particular contribution rates) should be occupation- and

gender-specific.