On a New Perspective in Longevity Risk Management: The Lifetime Shifting

Longer lives are an achievement and the course of lifespan is increasingly influenced by unobservable risk factors altering the chronological pace of aging. Then, the present work proposes an analytical approach to characterizing the human lifetime based on the concept of non-chronological age. Starting from a chronological Gompertz mortality framework, we define the non-chronological lifespan and characterize it probabilistically by deriving, in closed-form, the expression for the cumulative distribution function, the density of deaths function, and the mortality hazard function. We find that non-chronological death probabilities are a time-dependent affine transformation of chronological death probabilities for a newborn, and we highlight the link between the non-chronological lifetime and the concept of individual frailty in heterogeneous mortality modelling. We believe that our proposal may contribute to shaping a new perspective on longevity risk measurement and management.