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Optimal commutable annuities to minimize the probability of lifetime ruin

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  • Wang, Ting
  • Young, Virginia R.
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    Abstract

    We find the minimum probability of lifetime ruin of an investor who can invest in a market with a risky and a riskless asset and who can purchase a commutable life annuity. The surrender charge of a life annuity is a proportion of its value. Ruin occurs when the total of the value of the risky and riskless assets and the surrender value of the life annuity reaches zero. We find the optimal investment strategy and optimal annuity purchase and surrender strategies in two situations: (i) the value of the risky and riskless assets is allowed to be negative, with the imputed surrender value of the life annuity keeping the total positive; (ii) the value of the risky and riskless assets is required to be non-negative. In the first case, although the individual has the flexibility to buy or sell at any time, we find that the individual will not buy a life annuity unless she can cover all her consumption via the annuity and she will never sell her annuity. In the second case, the individual surrenders just enough annuity income to keep her total assets positive. However, in this second case, the individual’s annuity purchasing strategy depends on the size of the proportional surrender charge. When the charge is large enough, the individual will not buy a life annuity unless she can cover all her consumption, the so-called safe level. When the charge is small enough, the individual will buy a life annuity at a wealth lower than this safe level.

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    Bibliographic Info

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

    Volume (Year): 50 (2012)
    Issue (Month): 1 ()
    Pages: 200-216

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    Handle: RePEc:eee:insuma:v:50:y:2012:i:1:p:200-216

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

    Related research

    Keywords: Life annuities; Retirement; Optimal investment; Stochastic control; Free-boundary problem;

    References

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    1. Bayraktar, Erhan & Young, Virginia R., 2007. "Minimizing the probability of lifetime ruin under borrowing constraints," Insurance: Mathematics and Economics, Elsevier, vol. 41(1), pages 196-221, July.
    2. 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.
    3. Thomas Davidoff & Jeffrey R. Brown & Peter A. Diamond, 2003. "Annuities and Individual Welfare," NBER Working Papers 9714, National Bureau of Economic Research, Inc.
    4. Jeffrey R. Brown & Jeffrey R. Kling & Sendhil Mullainathan & Marian V. Wrobel, 2008. "Why Don’t People Insure Late-Life Consumption? A Framing Explanation of the Under-Annuitization Puzzle," American Economic Review, American Economic Association, vol. 98(2), pages 304-09, May.
    5. Jeffrey R. Brown, 2007. "Rational and Behavioral Perspectives on the Role of Annuities in Retirement Planning," NBER Working Papers 13537, National Bureau of Economic Research, Inc.
    6. Sachi Purcal & John Piggott, 2008. "Explaining Low Annuity Demand: An Optimal Portfolio Application to Japan," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 75(2), pages 493-516.
    7. Erhan Bayraktar & Virginia R. Young, 2008. "Minimizing the Probability of Ruin when Consumption is Ratcheted," Papers 0806.2358, arXiv.org.
    8. Julie R. Agnew & Lisa R. Anderson & Jeffrey R. Gerlach & Lisa R. Szykman, 2008. "Who Chooses Annuities? An Experimental Investigation of the Role of Gender, Framing, and Defaults," American Economic Review, American Economic Association, vol. 98(2), pages 418-22, May.
    9. Gerber, David S. & Weber, René, 2007. "Demography and investment behavior of pension funds: evidence for Switzerland," Journal of Pension Economics and Finance, Cambridge University Press, vol. 6(03), pages 313-337, November.
    10. Cannon, Edmund & Tonks, Ian, 2008. "Annuity Markets," OUP Catalogue, Oxford University Press, number 9780199216994, September.
    11. Milevsky, Moshe A. & Young, Virginia R., 2007. "Annuitization and asset allocation," Journal of Economic Dynamics and Control, Elsevier, vol. 31(9), pages 3138-3177, September.
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    Cited by:
    1. Wang, Ting & Young, Virginia R., 2012. "Maximizing the utility of consumption with commutable life annuities," Insurance: Mathematics and Economics, Elsevier, vol. 51(2), pages 352-369.

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