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Choosing the Optimal Annuitization Time Post Retirement

  • Russell Gerrard
  • Bjarne Højgaard
  • Elena Vigna
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    In the context of decision making for retirees of a defined contribution pension scheme in the de-cumulation phase, we formulate and solve a problem of finding the optimal time of annuitization for a retiree having the possibility of choosing her own investment and consumption strategy. We formulate the problem as a combined stochastic control and optimal stopping problem. As criterion for the optimization we select a loss function that penalizes both the deviance of the running consumption rate from a desired consumption rate and the deviance of the final wealth at the time of annuitization from a desired target. We find closed form solutions for the problem and show the existence of three possible types of solutions depending on the free parameters of the problem. In numerical applications we find the optimal wealth that triggers annuitization, compare it with the desired target and investigate its dependence on both parameters of the financial market and parameters linked to the risk attitude of the retiree. Simulations of the behaviour of the risky asset seem to show that under typical situations optimal annuitization should occur a few years after retirement.

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    File URL: http://www.carloalberto.org/assets/working-papers/no.76.pdf
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    Paper provided by Collegio Carlo Alberto in its series Carlo Alberto Notebooks with number 76.

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    Length: 32 pages
    Date of creation: 2008
    Date of revision:
    Handle: RePEc:cca:wpaper:76
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    1. 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.
    2. 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.
    3. Blake, David & Cairns, Andrew J. G. & Dowd, Kevin, 2003. "Pensionmetrics 2: stochastic pension plan design during the distribution phase," Insurance: Mathematics and Economics, Elsevier, vol. 33(1), pages 29-47, August.
    4. 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.
    5. Blake, David & Cairns, Andrew J. G. & Dowd, Kevin, 2001. "Pensionmetrics: stochastic pension plan design and value-at-risk during the accumulation phase," Insurance: Mathematics and Economics, Elsevier, vol. 29(2), pages 187-215, October.
    6. 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.
    7. Gabriele Stabile, 2006. "Optimal Timing Of The Annuity Purchase: Combined Stochastic Control And Optimal Stopping Problem," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 9(02), pages 151-170.
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