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DISCUSSION PAPER PI-1001

Bayesian Stochastic Mortality Modelling for Two Populations

Andrew Cairns, David Blake, Kevin Dowd, Guy Coughlan and Marwa Khalaf-Allah

The paper introduces a new framework for modelling the joint development over time
of mortality rates in a pair of related populations by combining a number of recent
and novel developments in stochastic mortality modelling. In doing so, the aim is
to produce consistent mortality forecasts for the two populations. First, and by way
of example, we develop an Age-Period-Cohort model which incorporates a mean-
reverting stochastic spread that allows for different trends in mortality improvement
rates in the short-run, but parallel improvements in the long run. Second, we fit
the model using a Bayesian framework that allows us to combine estimation of the
unobservable state variables and the parameters of the stochastic processes driving
them into a single procedure.

The framework is designed for large populations coupled with a small sub-population
and is applied to the England & Wales national and Continuous Mortality Investi-
gation assured lives males populations. We compare and contrast results based on
the two-population approach with single-population results.

Keywords: Small sub-populations, age effect, period effect, cohort effect, Markov
chain Monte Carlo, parameter uncertainty.