Heterogeneity in Survival Models - Applications to Pensions and Life Annuities

Abstract

The aim of this paper is to give an overview of the models used to represent heterogeneity in life insurance, with particular regard to pensions and life annuities.

First, heterogeneity due to risk factors observable at policy issue is considered. The underwriting process addresses at least some of these items, so that each contract can be assigned a premium rate consistent with its specific features. Heterogeneity models suitable to this regard can be looked at as individual valuation models.

Secondly, we focus on heterogeneity due to unobservable risk factors. These aspects, which usually are not embedded into the underwriting process, require collective valuation models.

Whilst individual heterogeneity models are well known in life insurance mathematics, collective models are not common. So the paper is in particular devoted to the latter. Their actuarial relevance is shown with some investigations concerning the life annuity business, where due to evolving mortality a more detailed representation of insured risks is recommended, so to reduce the possibility of biased valuations.

Keywords: frailty, risk factors, differential mortality models, standard and population mortality, actuarial valuation

JEL Classification: C00, G22, G23