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Optimal consumption and portfolio choice for pooled annuity funds

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  • Stamos, Michael Z.
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    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.

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    Bibliographic Info

    Article provided by Elsevier in its journal Insurance: Mathematics and Economics.

    Volume (Year): 43 (2008)
    Issue (Month): 1 (August)
    Pages: 56-68

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    Handle: RePEc:eee:insuma:v:43:y:2008:i:1:p:56-68

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    Web page: http://www.elsevier.com/locate/inca/505554

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    Cited by:
    1. 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.
    2. 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.
    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. Wolfram J. Horneff & Raimond H. Maurer, 2008. "Deferred Annuities and Strategic Asset Allocation," Working Papers wp178, University of Michigan, Michigan Retirement Research Center.
    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.

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