Bühlmann Credibility-Based Approaches to Modeling Mortality Rates for Multiple Populations

Abstract

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.