Quantifying the trade-off between income stability and the number of members in a pooled annuity fund

Thomas Bernhardt, Catherine Donnelly

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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.
Original languageEnglish
JournalASTIN Bulletin: The Journal of the IAA
Early online date22 Oct 2020
DOIs
Publication statusE-pub ahead of print - 22 Oct 2020

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