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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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    1. Vittas, Dimitri, 2011. "The mechanics and regulation of variable payout annuities," Policy Research Working Paper Series 5762, The World Bank.
    2. 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.
    3. 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.
    4. Olivia S. Mitchell, 1999. "New Evidence on the Money's Worth of Individual Annuities," American Economic Review, American Economic Association, vol. 89(5), pages 1299-1318, December.
    5. Alexander Braun & Nadine Gatzert & Hato Schmeiser, 2012. "Performance and Risks of Open‐End Life Settlement Funds," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 79(1), pages 193-230, March.
    6. 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.
    7. Lee Lockwood, 2012. "Bequest Motives and the Annuity Puzzle," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 15(2), pages 226-243, April.
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    Citations

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    Cited by:

    1. Milevsky, Moshe A. & Salisbury, Thomas S., 2015. "Optimal retirement income tontines," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 91-105.
    2. 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.
    3. repec:pal:gpprii:v:42:y:2017:i:3:d:10.1057_s41288-017-0056-1 is not listed on IDEAS
    4. 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.

    More about this item

    Keywords

    Longevity risk; Pensions; Pooled annuity fund;

    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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