a b s t r a c tWe introduce a model for the mortality rates of multiple populations. To build the proposed model we investigate to what extent a common age effect can be found among the mortality experiences of several countries and use a common principal component analysis to estimate a common age effect in an age-period model for multiple populations. The fit of the proposed model is then compared to age-period models fitted to each country individually, and to the fit of the model proposed by Li and Lee (2005).Although we do not consider stochastic mortality projections in this paper, we argue that the proposed common age effect model can be extended to a stochastic mortality model for multiple populations, which allows to generate mortality scenarios simultaneously for all considered populations. This is particularly relevant when mortality derivatives are used to hedge the longevity risk in an annuity portfolio as this often means that the underlying population for the derivatives is not the same as the population in the annuity portfolio.

We review a number of multi-population mortality models: variations of the Li and Lee (2005) model, and the common-age-effect (CAE) model of Kleinow (2014). Model parameters are estimated using maximum likelihood. Although this introduces some challenging identifiability problems and complicates the estimation process it allows a fair comparison of the different models. We propose to solve these identifiability problems by applying two dimensional constraints over the parameters. Using data from six countries, we compare and rank, both visually and numerically, the models' fitting qualities and develop forecasting models that produce nondiverging, joint mortality rate scenarios.It is found that the CAE model fits best. But we also find that the Li and Lee model potentially suffers from robustness problems when calibrated using maximum likelihood.

In this paper we review the Wilkie asset model for a variety of UK economic indices, including the Retail Prices Index, both without and with an ARCH model, the wages index, share dividend yields, share dividends and share prices, long term bond yields, short term bond yields and index-linked bond yields, in each case by updating the parameters to June 2009. We discuss how the model has performed from 1994 to 2009 and estimate the values of the parameters and their confidence intervals over various sub-periods to study their stability. Our analysis shows that the residuals of many of the series are much fatter-tailed than in a normal distribution. We observe also that besides the stochastic uncertainty built into the model by the random innovations there is also parameter uncertainty arising from the estimated values of the parameters.