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QUANTIFYING THE TRADE-OFF BETWEEN INCOME STABILITY AND THE NUMBER OF MEMBERS IN A POOLED ANNUITY FUND

Published online by Cambridge University Press:  22 October 2020

Thomas Bernhardt Open the ORCID record for Thomas Bernhardt [Opens in a new window]  and
Catherine Donnelly
Thomas Bernhardt
Affiliation:
Department of Mathematics, University of Michigan, Ann Arbor, Michigan, MI48109-1043, USA, E-Mail: bernt@umich.edu
Catherine Donnelly*
Affiliation:
Risk Insight Lab, Department of Actuarial Mathematics and Statistics, Heriot-Watt University, Edinburgh, EH14 4AS, UK, E-Mail: C.Donnelly@hw.ac.uk
*
E-Mail: C.Donnelly@hw.ac.uk
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Abstract

The number of people who receive a stable income for life from a closed pooled annuity fund is studied. Income stability is defined as keeping the income within a specified tolerance of the initial income in a fixed proportion of future scenarios. The focus is on quantifying the effect of the number of members, which drives the level of idiosyncratic longevity risk in the fund, on the income stability. To do this, investment returns are held constant, and systematic longevity risk is omitted. An analytical expression that closely approximates the number of fund members who receive a stable income is derived and is seen to be independent of the mortality model. An application of the result is to calculate the length of time for which the pooled annuity fund can provide the desired level of income stability.

Keywords

Longevity creditdecumulationtontineunsystematic riskpoolingG11G22
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 51 , Issue 1 , January 2021 , pp. 101 - 130
Copyright
© 2020 by Astin Bulletin. All rights reserved

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