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Analytic expressions for annuities based on Makeham–Beard mortality laws

Published online by Cambridge University Press:  28 April 2020

David C. Bowie
David C. Bowie*
Affiliation:
Hymans Robertson LLP, Exchange Place One, 1 Semple Street, Edinburgh, EH3 8BL, UK
*
*Corresponding author. E-mail: david.bowie@hymans.co.uk
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Abstract

This note derives analytic expressions for annuities based on a class of parametric mortality “laws” (the so-called Makeham–Beard family) that includes a logistic form that models a decelerating increase in mortality rates at the higher ages. Such models have been shown to provide a better fit to pensioner and annuitant mortality data than those that include an exponential increase. The expressions derived for evaluating single life and joint life annuities for the Makeham–Beard family of mortality laws use the Gauss hypergeometric function and Appell function of the first kind, respectively.

Keywords

AnnuitiesMakeham–Beard mortality lawGauss hypergeometric functionAppell function
Type
Paper
Information
Annals of Actuarial Science , Volume 15 , Issue 1 , March 2021 , pp. 1 - 13
Copyright
© Institute and Faculty of Actuaries 2020

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