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-inference setting for updating the parameters of the stochastic model according to the experienced mortality.
Life tables in actuarial models: from the deterministic setting to a Bayesian approach / A. Olivieri; E. Pitacco. - In: ASTA ADVANCES IN STATISTICAL ANALYSIS. - ISSN 1863-8171. - 96 (2)(2012), pp. 127-153. [10.1007/s10182-011-0177-y]