Clustering-Based Extensions of the Common Age Effect Multi-Population Mortality Model

Abstract

We introduce four variants of the common age effect model proposed by Kleinow, which describes the mortality rates of multiple populations. Our model extensions are based on the assumption of multiple common age effects, each of which is shared only by a subgroup of all considered populations. This makes the models more realistic while still keeping them as parsimonious as possible, improving the goodness of fit. We apply different clustering methods to identify suitable subgroups. Some of the algorithms are borrowed from the unsupervised learning literature, while others are more domain-specific. In particular, we propose and investigate a new model with fuzzy clustering, in which each population’s individual age effect is a linear combination of a small number of age effects. Due to their good interpretability, our clustering-based models also allow some insights in the historical mortality dynamics of the populations. Numerical results and graphical illustrations of the considered models and their performance in-sample as well as out-of-sample are provided.

Keywords

• mortality modeling and forecasting
• stochastic mortality model
• mortality of multiple populations
• common age effect model
• cluster analysis
• maximum likelihood estimation