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Exchanging uncertain mortality for a cost

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  • Donnelly, Catherine
  • Guillén, Montserrat
  • Nielsen, Jens Perch

Abstract

We analyze a pooled annuity fund from a participant’s perspective by comparing it to a mortality-linked fund, a type of variable payout life annuity, that gives a return linked to the force of mortality but subject to a cost. Fixing the instantaneous volatility of return on wealth, we find that the expected return on the pooled annuity fund is higher except when the costs are very low in the mortality-linked fund. Similar results are obtained when maximizing the expected lifetime utility of consumption, assuming a constant relative risk aversion utility function. In both settings, our results indicate that a participant may be willing to accept the mortality risk of the pooled annuity fund, even when only 100 individuals are pooling their mortality in the pooled annuity fund.

Suggested Citation

  • Donnelly, Catherine & Guillén, Montserrat & Nielsen, Jens Perch, 2013. "Exchanging uncertain mortality for a cost," Insurance: Mathematics and Economics, Elsevier, vol. 52(1), pages 65-76.
    • Handle: RePEc:eee:insuma:v:52:y:2013:i:1:p:65-76
    DOI: 10.1016/j.insmatheco.2012.11.001
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    References listed on IDEAS

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    Cited by:

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    2. Chen, An & Guillen, Montserrat & Rach, Manuel, 2021. "Fees in tontines," Insurance: Mathematics and Economics, Elsevier, vol. 100(C), pages 89-106.
    3. Milevsky, Moshe A. & Salisbury, Thomas S., 2015. "Optimal retirement income tontines," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 91-105.
    4. 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).
    5. Milevsky, Moshe A., 2020. "Calibrating Gompertz in reverse: What is your longevity-risk-adjusted global age?," Insurance: Mathematics and Economics, Elsevier, vol. 92(C), pages 147-161.
    6. Hieber, Peter & Lucas, Nathalie, 2020. "Life-Care Tontines," LIDAM Discussion Papers ISBA 2020026, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    7. Donnelly, Catherine & Guillén, Montserrat & Nielsen, Jens Perch, 2014. "Bringing cost transparency to the life annuity market," Insurance: Mathematics and Economics, Elsevier, vol. 56(C), pages 14-27.
    8. Cecilia Dassatti & Rodrigo Lluberas, 2020. "The costs of annuitising: are retirees fairly charged?," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan;The Geneva Association, vol. 45(3), pages 535-557, July.
    9. 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.
    10. Balter, Anne G. & Kallestrup-Lamb, Malene & Rangvid, Jesper, 2021. "Macro longevity risk and the choice between annuity products: Evidence from Denmark," Insurance: Mathematics and Economics, Elsevier, vol. 99(C), pages 355-362.
    11. 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.
    12. 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.
    13. Helena Chuliá & Montserrat Guillén & Jorge M. Uribe, 2015. "Mortality and Longevity Risks in the United Kingdom: Dynamic Factor Models and Copula-Functions," Working Papers 2015-03, Universitat de Barcelona, UB Riskcenter.
    14. Abdikerimova, Samal & Feng, Runhuan, 2022. "Peer-to-peer multi-risk insurance and mutual aid," European Journal of Operational Research, Elsevier, vol. 299(2), pages 735-749.

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    More about this item

    Keywords

    Longevity risk; Pensions; Pooled annuity fund;
    All these keywords.

    JEL classification:

    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies
    • G23 - Financial Economics - - Financial Institutions and Services - - - Non-bank Financial Institutions; Financial Instruments; Institutional Investors

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