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. 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 quantified by adopting the concept 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.
Keywords: Heterogeneity, Frailty, Risk factors, Force of mortality, Mortality laws, Parametric models, Special-rate annuities.