IDEAS home Printed from https://ideas.repec.org/a/eee/insuma/v64y2015icp91-105.html
   My bibliography  Save this article

Optimal retirement income tontines

Author

Listed:
  • Milevsky, Moshe A.
  • Salisbury, Thomas S.

Abstract

Tontines were once a popular type of mortality-linked investment pool. They promised enormous rewards to the last survivors at the expense of those died early. While this design appealed to the gambling instinct, it is a suboptimal way to generate retirement income. Indeed, actuarially-fair life annuities making constant payments–where the insurance company is exposed to longevity risk–induce greater lifetime utility. However, tontines do not have to be structured the historical way, i.e. with a constant cash flow shared amongst a shrinking group of survivors. Moreover, insurance companies do not sell actuarially-fair life annuities, in part due to aggregate longevity risk.

Suggested Citation

  • Milevsky, Moshe A. & Salisbury, Thomas S., 2015. "Optimal retirement income tontines," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 91-105.
  • Handle: RePEc:eee:insuma:v:64:y:2015:i:c:p:91-105
    DOI: 10.1016/j.insmatheco.2015.05.002
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167668715000748
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.insmatheco.2015.05.002?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. John Piggott & Emiliano A. Valdez & Bettina Detzel, 2005. "The Simple Analytics of a Pooled Annuity Fund," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 72(3), pages 497-520, September.
    2. Valdez, Emiliano A. & Piggott, John & Wang, Liang, 2006. "Demand and adverse selection in a pooled annuity fund," Insurance: Mathematics and Economics, Elsevier, vol. 39(2), pages 251-266, October.
    3. Weir, David R., 1989. "Tontines, Public Finance, and Revolution in France and England, 1688–1789," The Journal of Economic History, Cambridge University Press, vol. 49(1), pages 95-124, March.
    4. Menahem E. Yaari, 1965. "Uncertain Lifetime, Life Insurance, and the Theory of the Consumer," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 32(2), pages 137-150.
    5. Cannon, Edmund & Tonks, Ian, 2008. "Annuity Markets," OUP Catalogue, Oxford University Press, number 9780199216994.
    6. Andreas Richter & Frederik Weber, 2011. "Mortality-Indexed Annuities Managing Longevity Risk Via Product Design," North American Actuarial Journal, Taylor & Francis Journals, vol. 15(2), pages 212-236.
    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. Milevsky, Moshe A., 2014. "Portfolio choice and longevity risk in the late seventeenth century: a re-examination of the first English tontine," Financial History Review, Cambridge University Press, vol. 21(3), pages 225-258, December.
    9. Geoffrey Poitras, 2000. "The Early History of Financial Economics, 1478–1776," Books, Edward Elgar Publishing, number 2151.
    10. Chao Qiao & Michael Sherris, 2013. "Managing Systematic Mortality Risk With Group Self-Pooling and Annuitization Schemes," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 80(4), pages 949-974, December.
    11. 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.
    12. Rothschild, Casey G., 2009. "Adverse selection in annuity markets: Evidence from the British Life Annuity Act of 1808," Journal of Public Economics, Elsevier, vol. 93(5-6), pages 776-784, June.
    13. Stamos, Michael Z., 2008. "Optimal consumption and portfolio choice for pooled annuity funds," Insurance: Mathematics and Economics, Elsevier, vol. 43(1), pages 56-68, August.
    14. Goetzmann, William N. & Rouwenhorst, K. Geert (ed.), 2005. "The Origins of Value: The Financial Innovations that Created Modern Capital Markets," OUP Catalogue, Oxford University Press, number 9780195175714.
    15. Donnelly, Catherine, 2015. "Actuarial Fairness And Solidarity In Pooled Annuity Funds," ASTIN Bulletin, Cambridge University Press, vol. 45(1), pages 49-74, January.
    16. Nicholas C. Barberis, 2013. "Thirty Years of Prospect Theory in Economics: A Review and Assessment," Journal of Economic Perspectives, American Economic Association, vol. 27(1), pages 173-196, Winter.
    17. Min Dai & Yue Kuen Kwok & Jianping Zong, 2008. "Guaranteed Minimum Withdrawal Benefit In Variable Annuities," Mathematical Finance, Wiley Blackwell, vol. 18(4), pages 595-611, October.
    18. Pitacco, Ermanno & Denuit, Michel & Haberman, Steven & Olivieri, Annamaria, 2009. "Modelling Longevity Dynamics for Pensions and Annuity Business," OUP Catalogue, Oxford University Press, number 9780199547272.
    19. Ransom, Roger L. & Sutch, Richard, 1987. "Tontine Insurance and the Armstrong Investigation: A Case of Stifled Innovation, 1868–1905," The Journal of Economic History, Cambridge University Press, vol. 47(2), pages 379-390, June.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Chen, An & Guillen, Montserrat & Rach, Manuel, 2021. "Fees in tontines," Insurance: Mathematics and Economics, Elsevier, vol. 100(C), pages 89-106.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. Bravo, Jorge Miguel & El Mekkaoui de Freitas, Najat, 2018. "Valuation of longevity-linked life annuities," Insurance: Mathematics and Economics, Elsevier, vol. 78(C), pages 212-229.
    7. 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.
    8. 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.
    9. Thomas Bernhardt & Catherine Donnelly, 2019. "Modern tontine with bequest: innovation in pooled annuity products," Papers 1903.05990, arXiv.org.
    10. 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.
    11. Yikang Li & Casey Rothschild, 2020. "Selection and Redistribution in the Irish Tontines of 1773, 1775, and 1777," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 87(3), pages 719-750, September.
    12. 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.
    13. 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.
    14. Moshe A. Milevsky & Thomas S. Salisbury, 2024. "The Riccati Tontine: How to Satisfy Regulators on Average," Papers 2402.14555, arXiv.org.
    15. 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.
    16. 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.
    17. Annamaria Olivieri, 2021. "Designing Annuities with Flexibility Opportunities in an Uncertain Mortality Scenario," Risks, MDPI, vol. 9(11), pages 1-18, October.
    18. Kabuche, Doreen & Sherris, Michael & Villegas, Andrés M. & Ziveyi, Jonathan, 2024. "Pooling functional disability and mortality in long-term care insurance and care annuities: A matrix approach for multi-state pools," Insurance: Mathematics and Economics, Elsevier, vol. 116(C), pages 165-188.
    19. 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.
    20. 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).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:insuma:v:64:y:2015:i:c:p:91-105. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/505554 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.