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Actuarial Fairness And Solidarity In Pooled Annuity Funds

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  • Donnelly, Catherine

Abstract

Various types of structures that enable a group of individuals to pool their mortality risk have been proposed in the literature. Collectively, the structures are called pooled annuity funds. Since the pooled annuity funds propose different methods of pooling mortality risk, we investigate the connections between them and find that they are genuinely different for a finite heterogeneous membership profile. We discuss the importance of actuarial fairness, defined as the expected benefits equalling the contributions for each member, in the context of pooling mortality risk and comment on whether actuarial unfairness can be seen as solidarity between members. We show that, with a finite number of members in the fund, the group self-annuitization scheme is not actuarially fair: some members subsidize the other members. The implication is that the members who are subsidizing the others may obtain a higher expected benefit by joining a fund with a more favorable membership profile. However, we find that the subsidies are financially significant only for very small or highly heterogeneous membership profiles.

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  • Donnelly, Catherine, 2015. "Actuarial Fairness And Solidarity In Pooled Annuity Funds," ASTIN Bulletin, Cambridge University Press, vol. 45(1), pages 49-74, January.
    • Handle: RePEc:cup:astinb:v:45:y:2015:i:01:p:49-74_00
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    Cited by:

    1. Michel Denuit & Raluca Vernic, 2018. "Bivariate Bernoulli Weighted Sums and Distribution of Single-Period Tontine Benefits," Methodology and Computing in Applied Probability, Springer, vol. 20(4), pages 1403-1416, December.
    2. Annamaria Olivieri, 2021. "Designing Annuities with Flexibility Opportunities in an Uncertain Mortality Scenario," Risks, MDPI, vol. 9(11), pages 1-18, October.
    3. Shuanglan Li & Héloïse Labit Hardy & Michael Sherris & Andrés M. Villegas, 2022. "A Managed Volatility Investment Strategy for Pooled Annuity Products," Risks, MDPI, vol. 10(6), pages 1-30, June.
    4. Milevsky, Moshe A. & Salisbury, Thomas S., 2015. "Optimal retirement income tontines," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 91-105.
    5. Denuit, Michel & Robert, Christian Y., 2021. "From risk sharing to pure premium for a large number of heterogeneous losses," Insurance: Mathematics and Economics, Elsevier, vol. 96(C), pages 116-126.
    6. 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).
    7. Chen, An & Rach, Manuel, 2023. "Actuarial fairness and social welfare in mixed-cohort tontines," Insurance: Mathematics and Economics, Elsevier, vol. 111(C), pages 214-229.
    8. Milevsky, Moshe A. & Salisbury, Thomas S., 2016. "Equitable Retirement Income Tontines: Mixing Cohorts Without Discriminating," ASTIN Bulletin, Cambridge University Press, vol. 46(3), pages 571-604, September.
    9. Devolder, Pierre, 2019. "Une alternative a la pension a points : le compte individuel pension en euros," LIDAM Discussion Papers ISBA 2019011, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    10. Thomas Bernhardt & Ge Qu, 2021. "Wealth heterogeneity in a closed pooled annuity fund," Papers 2110.13467, arXiv.org, revised Aug 2022.
    11. Peter A. Forsyth & Kenneth R. Vetzal & G. Westmacott, 2022. "Optimal performance of a tontine overlay subject to withdrawal constraints," Papers 2211.10509, arXiv.org.
    12. Denuit, Michel, 2019. "Size-biased transform and conditional mean risk sharing, with application to P2P insurance and tontines," LIDAM Discussion Papers ISBA 2019010, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    13. Xie, Lin & Chen, Lv & Qian, Linyi & Li, Danping & Yang, Zhixin, 2023. "Optimal investment and consumption strategies for pooled annuity with partial information," Insurance: Mathematics and Economics, Elsevier, vol. 108(C), pages 129-155.
    14. Thomas Bernhardt & Catherine Donnelly, 2020. "Quantifying the trade-off between income stability and the number of members in a pooled annuity fund," Papers 2010.16009, arXiv.org.
    15. Graziella Caselli & Rosa Maria Lipsi, 2018. "Survival inequalities and redistribution in the Italian pension system," Vienna Yearbook of Population Research, Vienna Institute of Demography (VID) of the Austrian Academy of Sciences in Vienna, vol. 16(1), pages 083-110.
    16. Marcel Bräutigam & Montserrat Guillén & Jens P. Nielsen, 2017. "Facing Up to Longevity with Old Actuarial Methods: A Comparison of Pooled Funds and Income Tontines," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan;The Geneva Association, vol. 42(3), pages 406-422, July.
    17. Chen, An & Rach, Manuel, 2019. "Options on tontines: An innovative way of combining tontines and annuities," Insurance: Mathematics and Economics, Elsevier, vol. 89(C), pages 182-192.
    18. Thomas Bernhardt & Catherine Donnelly, 2019. "Modern tontine with bequest: innovation in pooled annuity products," Papers 1903.05990, arXiv.org.
    19. Moshe A. Milevsky & Thomas S. Salisbury, 2024. "The Riccati Tontine: How to Satisfy Regulators on Average," Papers 2402.14555, arXiv.org.
    20. Dagpunar, John, 2021. "Closed-form solutions for an explicit modern ideal tontine with bequest motive," Insurance: Mathematics and Economics, Elsevier, vol. 100(C), pages 261-273.
    21. Chen, An & Hieber, Peter & Rach, Manuel, 2021. "Optimal retirement products under subjective mortality beliefs," Insurance: Mathematics and Economics, Elsevier, vol. 101(PA), pages 55-69.
    22. Bernhardt, Thomas & Donnelly, Catherine, 2019. "Modern tontine with bequest: Innovation in pooled annuity products," Insurance: Mathematics and Economics, Elsevier, vol. 86(C), pages 168-188.
    23. Denuit, M. & Robert, C.Y., 2020. "From risk sharing to pure premium for a large number of heterogeneous losses," LIDAM Discussion Papers ISBA 2020015, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).

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