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1. Introduction
Understanding and quantifying mortality rates are fundamental to the study of the demography of human populations, and they are a basic input into actuarial calculations involving valuation and pricing of life insurance products. Since mortality rates have been observed to change over time, techniques to forecast future mortality rates are important within both demography and actuarial science. Two well-known examples of these techniques are the Lee–Carter (LC) (Lee & Carter 1992) and the Cairns–Blake–Dowd (CBD) (Cairns et al. 2006) models, which forecast mortality rates in two steps: firstly, a low dimensional summary of past mortality rates is constructed by fitting statistical models to historical mortality data, and secondly, future mortality rates are forecasted by extrapolating the summarised mortality rates into the future using time series models.
The LC and CBD models were applied originally to single populations. If forecasts for multiple populations were required, then the models were fit to each population separately. However, for several reasons, it seems reasonable to expect that a multi-population mortality forecasting model would produce more robust forecasts of future mortality rates than those produced by single-population models. If changes in mortality in a group of countries are due to common factors such as similar socioeconomic circumstances, shared improvements in public health and medical technology, then it makes sense to forecast the mortality rates for these countries as a group. Furthermore, mortality trends that are common to several populations would likely be captured with more statistical credibility in a model that relies on the experience of many countries, see Li & Lee (2005). Thus, Li & Lee (2005) recommend that multi-population models should be used even if the ultimate interest is only in forecasts for a single population. In addition, mortality forecasts from separate single-population models may diverge from each other, leading to implausible results if used in actuarial and demographic models, whereas a multi-population model can produce coherent forecasts. To this end, multi-population variants of the LC and CBD models have recently been developed.
In this work, we concentrate on the LC model and its multi-population extensions. We describe their design and fitting which have caused several challenges in the past. The original LC model cannot be fit as a regular regression model due to the...