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Quantifying The Trade-Off Between Income Stability And The Number Of Members In A Pooled Annuity Fund

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  • Bernhardt, Thomas
  • Donnelly, Catherine

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.

Suggested Citation

  • Bernhardt, Thomas & Donnelly, Catherine, 2021. "Quantifying The Trade-Off Between Income Stability And The Number Of Members In A Pooled Annuity Fund," ASTIN Bulletin, Cambridge University Press, vol. 51(1), pages 101-130, January.
    • Handle: RePEc:cup:astinb:v:51:y:2021:i:1:p:101-130_4
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    Cited by:

    1. Denuit, Michel & Robert, Christian Y., 2023. "Endowment contingency funds for mutual aid and public financing," LIDAM Discussion Papers ISBA 2023009, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    2. Thomas Bernhardt & Ge Qu, 2021. "Wealth heterogeneity in a closed pooled annuity fund," Papers 2110.13467, arXiv.org, revised Aug 2022.

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