Heterogeneity in mortality: a survey with an actuarial focus

Abstract

Heterogeneity in mortality is due to differences among the individuals, which are caused by various risk factors. Some risk factors are observable while others are unobservable. The set of observable risk factors clearly depends on the type of population addressed. The impact of observable risk factors on individual mortality, in particular when they also constitute “rating factors” in the calculation of premiums and other actuarial values, is usually expressed approximately, according to some pragmatic approach. For example, additive or multiplicative adjustments to the average age-specific mortality are frequently adopted. Heterogeneity due to unobservable risk factors can conversely be expressed by adopting the concept of individual “frailty”, which, however, can be interpreted and consequently modeled in several ways, according to the causes which are considered as originating the frailty itself: congenital characteristics, environmental features, lifestyle aspects, etc. In this paper, we provide a survey of scientific contributions on heterogeneity in mortality, focusing on modeling both observable and unobservable heterogeneity. We start with an overview of methodological contributions to heterogeneity and frailty modeling, coming from both the demographical and the actuarial context. We then shift to contributions analyzing the impact of frailty, in its various interpretations, on the results (cash flows, profits, etc.) of life insurance and life annuity portfolios and related risk profiles.