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A calendar year mortality model in continuous time

Published online by Cambridge University Press:  22 February 2023

Donatien Hainaut Open the ORCID record for Donatien Hainaut [Opens in a new window]
Donatien Hainaut*
Affiliation:
UCLouvain, LIDAM-ISBA, Voie du Roman Pays 20, 1348 Louvain-la-Neuve, Belgium
*
E-Mail: donatien.hainaut@uclouvain.be
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Abstract

This article proposes a continuous time mortality model based on calendar years. Mortality rates belong to a mean-reverting random field indexed by time and age. In order to explain the improvement of life expectancies, the reversion level of mortality rates is the product of a deterministic function of age and of a decreasing jump-diffusion process driving the evolution of longevity. We provide a general closed-form expression for survival probabilities and develop it when the mean reversion level of mortality rates is proportional to a Gompertz–Makeham law. We develop an econometric estimation method and validate the model on the Belgian population.

Keywords

Mortality rateslongevitysurvival probabilities
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 53 , Issue 2 , May 2023 , pp. 351 - 376
Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of The International Actuarial Association

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