The IA|BE 2015 Mortality Projection for the Belgian Population

Abstract

Life insurers, pension funds, health care providers and social security institutions face increasing expenses due to continuing improvements of mortality rates. The quantification of longevity risk in a systematic way requires stochastic mortality projection models, as Barrieu et al. (2012) indicate. The development of such models receives wide coverage in the actuarial, demographic and statistical literature, starting from the seminal work by Lee & Carter ([LC]) (Lee and Carter (1992)). As a follow-up to the 2002 mortality study of the former KVBA-ARAB (now: Institute of Actuaries in Belgium [IA|BE]) (see Lambrechts (2001), Brouhns et al. (2002a), Delfosse and Boelen (2002)), this report presents the set-up and technical specifications of the 2015 mortality projection model of the Institute of Actuaries in Belgium. The report also documents the resulting projections and the use of this model in actuarial applications. The IA|BE 2015 mortality projection model is a fully stochastic projection model of Li & Lee ([LL]) type, see Li and Lee (2005). The model is an application of the AG 2014 projection methodology of the Dutch Koninklijk Actuarieel Genootschap (see Koninklijk Actuarieel Genootschap (2014)) to the Belgian setting. This multi-population model projects Belgian mortality rates using Belgian mortality data together with observed mortality statistics for a collection of European countries with similar socioeconomic characteristics. A Lee & Carter model is imposed for the European mortality trend as well as for the Belgian deviation from this common trend. We have chosen this model as the preferred model from a comparative analysis of stochastic projection models proposed in recent scientific literature. As part of this comparative exercise we studied the single population mortality models from the papers by Cairns et al. (2009), Haberman and Renshaw (2011), Borger et al. (2014), Van Berkum et al. (2014), and the multi-population mortality models of Li and Lee (2005) and Koninklijk Actuarieel Genootschap (2014). The Cairns et al. (2006) stochastic two factor mortality model, and its generalizations proposed in Cairns et al. (2009), have not been investigated, since these Cairns, Blake & Dowd ([CBD]) mortality models are designed for pensioner age mortality only, whereas the IA|BE study puts focus on a projection model for the full age range (starting from age 0). For each model in the study we carefully examined its calibration, the modelling and projection of time dependent parameters and the produced forecasts. We evaluated the collection of mortality models using the criteria proposed in Cairns et al. (2009), supplemented with our own points of attention regarding biological reasonableness, statistical performance and transparency. The preferred model, and its calibration methodology, follows the AG2014 projection methodology as described in Koninklijk Actuarieel Genootschap (2014). Readers may want to consult the Koninklijk Actuarieel Genootschap (2014) documentation as additional reading material.This report is organized as follows. A technical description of the model is in Section 2. The subsections 2.1, 2.3 and 2.4 follow to a large extent Appendix A in Koninklijk Actuarieel Genootschap (2014). The use of the model and its applications are documented in Section 3. Section 4 concludes. Parameter estimates and the resulting IA|BE 2015 mortality projection for Belgium are available in an online appendix.