No abstract

While many of the prevalent stochastic mortality models provide adequate short- to medium-term forecasts, only few provide biologically plausible descriptions of mortality on longer horizons and are sufficiently stable to be of practical use in smaller populations. Among the very first to address the issue of modelling adult mortality in small populations was the SAINT model, which has been used for pricing, reserving and longevity risk management by the Danish Labour Market Supplementary Pension Fund (ATP) for more than a decade. The lessons learned have broadened our understanding of desirable model properties from the practitioner’s point of view and have led to a revision of model components to address accuracy, stability, flexibility, explainability and credibility concerns. This paper serves as an update to the original version published 10 years ago and presents the SAINT model with its modifications and the rationale behind them. The main improvement is the generalization of frailty models from deterministic structures to a flexible class of stochastic models. We show by example how the SAINT framework is used for modelling mortality at ATP and make comparisons to the Lee-Carter model.

The main purpose of coherent mortality models is to produce plausible, joint forecasts for related populations avoiding, e.g., crossing or diverging mortality trajectories; however, the coherence assumption is very restrictive and it enforces trends that may be at odds with data. In this paper we focus on coherent, two-sex mortality models and we prove, under suitable conditions, that the coherence assumption implies sex gap unimodality, i.e., we prove that the difference in life expectancy between women and men will first increase and then decrease. Moreover, we demonstrate that, in the model, the sex gap typically peaks when female life expectancy is between 30 to 50 years. This explains why coherent mortality models predict narrowing sex gaps for essentially all Western European countries and all jump-off years since the 1950s, despite the fact that the actual sex gap was widening until the 1980s. In light of these findings, we discuss the current role of coherence as the gold standard for multi-population mortality models.