Abstract

We provide a survey of scientific contributions on mortality heterogeneity, focusing in particular on “unobservable” heterogeneity and the related impact on the results (cash flows, profits, etc.) of life insurance and life annuity business.

Heterogeneity of a population in respect of 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 (for example: national populations vs insurance portfolios). It is worth noting that, whatever the type of population concerned, a residual heterogeneity remains because of unobservable factors.

The impact of observable risk factors on individual mortality, in particular when they also constitute “rating factors” in the calculation of actuarial values, is usually expressed approximately, according to some pragmatic approach.

Conversely, heterogeneity due to unobservable risk factors can be quantified in terms of individual “frailty”. However, individual frailty 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. It follows that the individual frailty can, in particular, be assumed either constant or variable throughout the lifetime.

The survey starts with an overview of methodological contributions to heterogeneity and frailty modeling, coming from both the demographical and the actuarial context, then shifting to contributions analyzing the impact of frailty, in its various interpretations, on life insurance and life annuity portfolios and related risk profiles.