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Egalitarian pooling and sharing of longevity risk a.k.a. can an administrator help skin the tontine cat?

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  • Dhaene, Jan
  • Milevsky, Moshe A.

Abstract

This paper is concerned with the mathematical problem of allocating longevity-linked fund payouts in a pool where participants differ in both wealth (contributions) and health (mortality), particularly when these groups are relatively small in size. In other words, we offer a modelling framework for distributing longevity-risk pools' income and benefits (or “tontine winnings”) when participants are heterogeneous. Similar to the nascent literature on decentralized risk sharing (DRS), there are several equally plausible arrangements for sharing benefits (a.k.a. “skinning the tontine cat”) among survivors. We argue that the selected rule may depend on the extent of social cohesion within the longevity risk pool, ranging from solidarity and altruism to pure individualism. And, if actuarial fairness is a concern, we suggest introducing an administrator – which differs from a guarantor – to make the tontine pool payouts collectively actuarial fair. Fairness is in the sense that the group of participants will on average receive the same benefits as they collectively invested; and we provide the mathematical framework to implement that suggestion. One thing is for certain: actuarial science cannot offer design uniqueness for longevity-contingent claims; only a consistent methodology.

Suggested Citation

  • Dhaene, Jan & Milevsky, Moshe A., 2024. "Egalitarian pooling and sharing of longevity risk a.k.a. can an administrator help skin the tontine cat?," Insurance: Mathematics and Economics, Elsevier, vol. 119(C), pages 238-250.
    • Handle: RePEc:eee:insuma:v:119:y:2024:i:c:p:238-250
    DOI: 10.1016/j.insmatheco.2024.09.003
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    References listed on IDEAS

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    1. Bravo, Jorge M. & Ayuso, Mercedes & Holzmann, Robert & Palmer, Edward, 2023. "Intergenerational actuarial fairness when longevity increases: Amending the retirement age," Insurance: Mathematics and Economics, Elsevier, vol. 113(C), pages 161-184.
    2. Denuit, Michel & Dhaene, Jan, 2012. "Convex order and comonotonic conditional mean risk sharing," Insurance: Mathematics and Economics, Elsevier, vol. 51(2), pages 265-270.
    3. 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.
    4. Milevsky, Moshe A. & Salisbury, Thomas S., 2015. "Optimal retirement income tontines," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 91-105.
    5. 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.
    6. Benjamin K. Couillard & Christopher L. Foote & Kavish Gandhi & Ellen Meara & Jonathan Skinner, 2021. "Rising Geographic Disparities in US Mortality," Journal of Economic Perspectives, American Economic Association, vol. 35(4), pages 123-146, Fall.
    7. Denuit, Michel & Hieber, Peter & Robert, Christian Y., 2022. "Mortality Credits Within Large Survivor Funds," ASTIN Bulletin, Cambridge University Press, vol. 52(3), pages 813-834, September.
    8. Michel Denuit & Jan Dhaene & Christian Y. Robert, 2022. "Risk‐sharing rules and their properties, with applications to peer‐to‐peer insurance," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 89(3), pages 615-667, September.
    9. 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.
    10. 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.
    11. repec:osf:osfxxx:8wbdv_v1 is not listed on IDEAS
    12. Kevin Milligan & Tammy Schirle, 2021. "The evolution of longevity: Evidence from Canada," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 54(1), pages 164-192, February.
    13. Chen, An & Chen, Yusha & Xu, Xian, 2022. "Care-dependent tontines," Insurance: Mathematics and Economics, Elsevier, vol. 106(C), pages 69-89.
    14. 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.
    15. Dhaene, Jan & Denuit, Michel, 1999. "The safest dependence structure among risks," Insurance: Mathematics and Economics, Elsevier, vol. 25(1), pages 11-21, September.
    16. David Blake & Tom Boardman & Andrew Cairns, 2014. "Sharing Longevity Risk: Why Governments Should Issue Longevity Bonds," North American Actuarial Journal, Taylor & Francis Journals, vol. 18(1), pages 258-277.
    17. Thomas Bernhardt & Catherine Donnelly, 2019. "Modern tontine with bequest: innovation in pooled annuity products," Papers 1903.05990, arXiv.org.
    18. Denuit, Michel & Hieber, Peter & Robert, Christian Y., 2022. "Mortality credits within large survivor funds," LIDAM Reprints ISBA 2022030, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    19. Cheung, Ka Chun & Lo, Ambrose, 2014. "Characterizing mutual exclusivity as the strongest negative multivariate dependence structure," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 180-190.
    20. Sloan, F.A. & Ayyagari, P. & Salm, M. & Grossman, D., 2010. "The longevity gap between black and white men in the united states at the beginning and end of the 20th century," American Journal of Public Health, American Public Health Association, vol. 100(2), pages 357-363.
    21. 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).
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