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Optimal consumption and portfolio choice for pooled annuity funds

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  • Stamos, Michael Z.

Abstract

This paper presents the optimal continuous time dynamic consumption and portfolio choice for pooled annuity funds. A pooled annuity fund constitutes an alternative way to protect against mortality risk compared to purchasing a life annuity. The crucial difference between the pooled annuity fund and purchase of a life annuity offered by an insurance company is that participants of a pooled annuity fund still have to bear some mortality risk while insured annuitants bear no mortality risk at all. The population of the pool is modelled by employing a Poisson process with time-dependent hazard-rate. It follows that the pool member's optimization problem has to account for the stochastic investment horizon and for jumps in wealth which occur if another pool member dies. In case the number of pool members goes to infinity analytical solutions are provided. For finite pool sizes the solution of the optimization problem is reduced to the numerical solution of a set of ODEs. A simulation and welfare analysis show that pooled annuity funds insure very effectively against longevity risk even if their pool size is rather small. Only very risk averse investors or those without access to small pools are more inclined to pay a risk premium to access private life annuity markets in order to lay off mortality risk completely. As even families constitute such small pools the model provides theoretical justification for the low empirical annuity demand.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:insuma:v:43:y:2008:i:1:p:56-68
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    References listed on IDEAS

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    1. Brown, Jeffrey R. & Mitchell, Olivia S. & Poterba, James M. & Warshawsky, Mark J., 2001. "The Role of Annuity Markets in Financing Retirement," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262529130, January.
    2. Abel, Andrew B & Warshawsky, Mark, 1988. "Specification of the Joy of Giving: Insights from Altruism," The Review of Economics and Statistics, MIT Press, vol. 70(1), pages 145-149, February.
    3. Kotlikoff, Laurence J & Summers, Lawrence H, 1981. "The Role of Intergenerational Transfers in Aggregate Capital Accumulation," Journal of Political Economy, University of Chicago Press, vol. 89(4), pages 706-732, August.
    4. Hurd, Michael D, 1989. "Mortality Risk and Bequests," Econometrica, Econometric Society, vol. 57(4), pages 779-813, July.
    5. 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.
    6. Bernheim, B Douglas & Shleifer, Andrei & Summers, Lawrence H, 1986. "The Strategic Bequest Motive," Journal of Labor Economics, University of Chicago Press, vol. 4(3), pages 151-182, July.
    7. 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.
    8. Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December.
    9. Horneff, Wolfram J. & Maurer, Raimond H. & Mitchell, Olivia S. & Dus, Ivica, 2008. "Following the rules: Integrating asset allocation and annuitization in retirement portfolios," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 396-408, February.
    10. Cairns, Andrew J.G. & Blake, David & Dowd, Kevin, 2006. "Stochastic lifestyling: Optimal dynamic asset allocation for defined contribution pension plans," Journal of Economic Dynamics and Control, Elsevier, vol. 30(5), pages 843-877, May.
    11. Wolfram Horneff & Raimond Maurer & Olivia Mitchell & Michael Stamos, 2007. "Money in Motion: Dynamic Portfolio Choice in Retirement," Working Papers wp152, University of Michigan, Michigan Retirement Research Center.
    12. Joao F. Cocco, 2005. "Consumption and Portfolio Choice over the Life Cycle," Review of Financial Studies, Society for Financial Studies, vol. 18(2), pages 491-533.
    13. Richard, Scott F., 1975. "Optimal consumption, portfolio and life insurance rules for an uncertain lived individual in a continuous time model," Journal of Financial Economics, Elsevier, vol. 2(2), pages 187-203, June.
    14. Albrecht, Peter & Maurer, Raimond, 2001. "Self-Annuitization, Ruin Risk in Retirement and Asset Allocation: The Annuity Benchmark," Sonderforschungsbereich 504 Publications 01-35, Sonderforschungsbereich 504, Universität Mannheim;Sonderforschungsbereich 504, University of Mannheim.
    15. Francisco Gomes & Alexander Michaelides, 2005. "Optimal Life-Cycle Asset Allocation: Understanding the Empirical Evidence," Journal of Finance, American Finance Association, vol. 60(2), pages 869-904, April.
    16. Thomas Davidoff & Jeffrey R. Brown & Peter A. Diamond, 2005. "Annuities and Individual Welfare," American Economic Review, American Economic Association, vol. 95(5), pages 1573-1590, December.
    17. Hurd, Michael D, 1987. "Savings of the Elderly and Desired Bequests," American Economic Review, American Economic Association, vol. 77(3), pages 298-312, June.
    18. Ho, Kwok & Milevsky, Moshe Arye & Robinson, Chris, 1994. "Asset allocation, life expectancy and shortfall," Financial Services Review, Elsevier, vol. 3(2), pages 109-126.
    19. Milevsky, Moshe Arye & Ho, Kwok & Robinson, Chris, 1997. "Asset Allocation via the Conditional First Exit Time or How to Avoid Outliving Your Money," Review of Quantitative Finance and Accounting, Springer, vol. 9(1), pages 53-70, July.
    20. Wolfram Horneff & Raimond Maurer & Michael Stamos, 2006. "Life-Cycle Asset Allocation with Annuity Markets: Is Longevity Insurance a Good Deal?," Working Papers wp146, University of Michigan, Michigan Retirement Research Center.
    21. Hato Schmeiser & Thomas Post, 2005. "Life Annuity Insurance Versus Self-Annuitization: An Analysis From the Perspective of the Family," Risk Management and Insurance Review, American Risk and Insurance Association, vol. 8(2), pages 239-255, September.
    22. Albrecht, Peter & Maurer, Raimond, 2002. "Self-Annuitization, Consumption Shortfall in Retirement and Asset Allocation: The Annuity Benchmark," Journal of Pension Economics and Finance, Cambridge University Press, vol. 1(03), pages 269-288, November.
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    Cited by:

    1. Wolfram J. Horneff & Raimond H. Maurer, 2008. "Deferred Annuities and Strategic Asset Allocation," Working Papers wp178, University of Michigan, Michigan Retirement Research Center.
    2. Chao Qiao & Michael Sherris, 2011. "Managing Systematic Mortality Risk with Group Self Pooling and Annuitisation Schemes," Working Papers 201104, ARC Centre of Excellence in Population Ageing Research (CEPAR), Australian School of Business, University of New South Wales.
    3. 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.
    4. Moshe A. Milevsky & Thomas S. Salisbury, 2016. "Optimal retirement income tontines," Papers 1610.10078, arXiv.org.
    5. Hanewald, Katja & Piggott, John & Sherris, Michael, 2013. "Individual post-retirement longevity risk management under systematic mortality risk," Insurance: Mathematics and Economics, Elsevier, vol. 52(1), pages 87-97.
    6. Milevsky, Moshe A. & Salisbury, Thomas S., 2015. "Optimal retirement income tontines," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 91-105.
    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. repec:pal:gpprii:v:42:y:2017:i:3:d:10.1057_s41288-017-0056-1 is not listed on IDEAS
    9. M. A. Milevsky & T. S. Salisbury, 2016. "Equitable retirement income tontines: Mixing cohorts without discriminating," Papers 1610.09384, arXiv.org.
    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.

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