Tang et al. (2022) propose a new class of models for stochastic mortality modelling using Hermite splines. There are four useful features of this class that are worth emphasising. First, for single-sex datasets, this new class of projection models can be fitted as a generalised linear model. Second, these models can automatically extrapolate mortality rates to ages above the maximum age of the data set. Third, simpler sub-variants of the models exist for forecasting when one of the variables lacks a clear drift. Finally, a minor reparameterisation increases the quality of long-range forecasts of period mortality.

One complication in mortality modelling is capturing the impact of risk factors that contribute to mortality differentials between different populations. Evidence has suggested that mortality differentials tend to diminish over age. Classical methods such as the Gompertz law attempt to capture mortality patterns over age using intercept and slope parameters, possibly causing an unjustified mortality crossover at advanced ages when applied independently to different populations. In recent research, Richards (Scandinavian Actuarial Journal 2020(2), 110–127) proposed a Hermite spline (HS) model that describes the age pattern of mortality differentials using one parameter and circumvents an unreasonable crossover by default. The original HS model was applied to pension data at individual level in the age dimension only. This paper extends the method to model population mortality in both age and period dimensions. Our results indicate that in addition to possessing desirable fitting properties, the HS approach can produce accurate mortality forecasts, compared with the Gompertz and P-splines models.

We investigate the link between death rates and smoking prevalence in ten developed countries with the aim of using smoking prevalence data to explain differences in country-specific death rates. A particular problem in building a stochastic mortality model based on smoking prevalence is that there are in general no separate mortality data for smokers and non-smokers available. We show how we can estimate mortality rates for smokers and non-smokers using information about the smoking prevalence in a number of developed countries, and making an additional assumption about the death rates of smokers. We consider this empirical investigation to be the first step towards a consistent mortality model for multiple populations, which will require modelling of country specific differences in mortality, as well as non-smokers’ and smokers’ mortality rates.