Incorporating hierarchical credibility theory into modelling of multi-country mortality rates

Abstract

A hierarchical credibility model is a generalization of the Bühlmann credibility model and the Bühlmann–Straub credibility model with a tree structure of four or more levels. This paper aims to incorporate hierarchical credibility theory, which is used in property and casualty insurance, to model multi-country mortality rates. The forecasting performances of the three/four/five-level hierarchical credibility models are compared with those of the classical Lee–Carter model and its three extensions for multiple populations (the joint- k, the co-integrated, and the augmented common factor Lee–Carter models). Numerical illustrations based on mortality data from the Human Mortality Database for both genders of the US, the UK and Japan with a series of fitting year spans and three forecasting periods show that the hierarchical credibility approach contributes to more accurate forecasts measured by the AMAPE (average of mean absolute percentage errors). Finally, a stochastic version of the proposed hierarchical credibility mortality model is also proposed, which can be used to construct predictive intervals on the projected mortality rates and to conduct stochastic simulations for applications.