Life Tables in Actuarial Models: From the Deterministic Setting to a Bayesian Approach

Abstract

The mortality dynamics experienced in the latest decades, especially at adult and old ages, has motivated the introduction of major innovations in the modeling of mortality for actuarial applications; such innovations concern, in particular, the representation of the uncertainty relating to aggregate mortality.

In this paper, we first provide a description of the traditional mortality model, which is deterministic, but also allows quite easily for a representation of the uncertainty relating to individual mortality. Then, we discuss a stochastic approach to the modeling of the uncertainty relating to aggregate mortality. Due to the importance of mortality evolution in respect of post-retirement liabilities, we refer to a portfolio of immediate life annuities (or pension annuities). We assume that a (projected) life table which provides a best-estimate assessment of annuitants' future mortality is available. We show that the life table, from which a deterministic description of future mortality can be obtained, can be used as the basic input of appropriate stochastic models. In particular, we consider a Bayesian-inferential setting for updating the parameters of the stochastic model according to the experienced mortality.

Keywords: Deterministic mortality, Stochastic mortality, Life annuities, Random fluctuations, Systematic deviations, Process risk, Uncertainty risk, Longevity risk, Bayesian inference

JEL Classification: C00, G22