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Choosing the optimal annuitization time post-retirement

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Author Info

  • Russell Gerrard
  • Bjarne H�jgaard
  • Elena Vigna
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    Abstract

    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://hdl.handle.net/10.1080/14697680903358248
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    Bibliographic Info

    Article provided by Taylor & Francis Journals in its journal Quantitative Finance.

    Volume (Year): 12 (2012)
    Issue (Month): 7 (September)
    Pages: 1143-1159

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    Handle: RePEc:taf:quantf:v:12:y:2012:i:7:p:1143-1159

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    Web page: http://www.tandfonline.com/RQUF20

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    Cited by:
    1. Marina Di Giacinto & Salvatore Federico & Fausto Gozzi & Elena Vigna, 2012. "Income drawdown option with minimum guarantee," Carlo Alberto Notebooks 272, Collegio Carlo Alberto.
    2. Yao, Haixiang & Yang, Zhou & Chen, Ping, 2013. "Markowitz’s mean–variance defined contribution pension fund management under inflation: A continuous-time model," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 851-863.
    3. Yao, Haixiang & Lai, Yongzeng & Ma, Qinghua & Jian, Minjie, 2014. "Asset allocation for a DC pension fund with stochastic income and mortality risk: A multi-period mean–variance framework," Insurance: Mathematics and Economics, Elsevier, vol. 54(C), pages 84-92.

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