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.
Inspired by the ideas of the joint-k, the co-integrated, the common factor, and the augmented common factor Lee-Carter models, in this article, we propose four corresponding Bühlmann ...credibility-based mortality models for multiple populations. Our models and the four Lee-Carter models are fitted with mortality data from the Human Mortality Database for both genders of the United States, the United Kingdom, and Japan to forecast mortality rates for three forecasting periods. Based on the measure of AMAPE (average of mean absolute percentage error), numerical illustrations show that our Bühlmann credibility-based models contribute to more accurate forecasts than the Lee-Carter-based models in all three forecasting periods. Finally, we also propose a stochastic version of the multi-population Bühlmann credibility-based mortality models, which can be used to construct predictive intervals on the projected mortality rates and to conduct stochastic simulations for applications.
