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Choosing the optimal annuitization time post-retirement

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  • Russell Gerrard
  • Bjarne Højgaard
  • Elena Vigna

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.

Suggested Citation

  • Russell Gerrard & Bjarne Højgaard & Elena Vigna, 2012. "Choosing the optimal annuitization time post-retirement," Quantitative Finance, Taylor & Francis Journals, vol. 12(7), pages 1143-1159, September.
    • Handle: RePEc:taf:quantf:v:12:y:2012:i:7:p:1143-1159
    DOI: 10.1080/14697680903358248
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    Citations

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    Cited by:

    1. 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.
    2. Jason S. Anquandah & Leonid V. Bogachev, 2019. "Optimal Stopping and Utility in a Simple Model of Unemployment Insurance," Papers 1902.06175, arXiv.org, revised Sep 2019.
    3. Alessandro Milazzo & Elena Vigna, 2018. "The Italian Pension Gap: A Stochastic Optimal Control Approach," Risks, MDPI, vol. 6(2), pages 1-20, April.
    4. Tiziano Angelis & Gabriele Stabile, 2019. "On the free boundary of an annuity purchase," Finance and Stochastics, Springer, vol. 23(1), pages 97-137, January.
    5. Di Giacinto, Marina & Federico, Salvatore & Gozzi, Fausto & Vigna, Elena, 2014. "Income drawdown option with minimum guarantee," European Journal of Operational Research, Elsevier, vol. 234(3), pages 610-624.
    6. Maria Alexandrova & Nadine Gatzert, 2019. "What Do We Know About Annuitization Decisions?," Risk Management and Insurance Review, American Risk and Insurance Association, vol. 22(1), pages 57-100, March.
    7. Masashi Ieda & Takashi Yamashita & Yumiharu Nakano, 2013. "A liability tracking approach to long term management of pension funds," Papers 1303.3956, arXiv.org.
    8. 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.
    9. Alessandra Milazzo & Elena Vigna, 2018. "The Italian Pension Gap: a Stochastic Optimal Control Approach," Carlo Alberto Notebooks 553, Collegio Carlo Alberto.
    10. Bernhardt, Thomas & Donnelly, Catherine, 2019. "Modern tontine with bequest: Innovation in pooled annuity products," Insurance: Mathematics and Economics, Elsevier, vol. 86(C), pages 168-188.
    11. Alessandro Milazzo & Elena Vigna, 2018. "“The Italian Pension Gap: a Stochastic Optimal Control Approach"," CeRP Working Papers 179, Center for Research on Pensions and Welfare Policies, Turin (Italy).
    12. Jason S. Anquandah & Leonid V. Bogachev, 2019. "Optimal Stopping and Utility in a Simple Modelof Unemployment Insurance," Risks, MDPI, vol. 7(3), pages 1-41, September.
    13. Hainaut, Donatien & Deelstra, Griselda, 2014. "Optimal timing for annuitization, based on jump diffusion fund and stochastic mortality," Journal of Economic Dynamics and Control, Elsevier, vol. 44(C), pages 124-146.
    14. Alessandro Milazzo & Elena Vigna, 2018. "The Italian Pension Gap: a Stochastic Optimal Control Approach," Papers 1804.05354, arXiv.org.
    15. Miloš Kopa & Vittorio Moriggia & Sebastiano Vitali, 2018. "Individual optimal pension allocation under stochastic dominance constraints," Annals of Operations Research, Springer, vol. 260(1), pages 255-291, January.
    16. Hassan Dadashi, 2018. "Optimal investment-consumption problem: post-retirement with minimum guarantee," Papers 1803.00611, arXiv.org, revised Aug 2020.
    17. Xiang Gao & Cody Hyndman & Traian A. Pirvu & Petar Jevti'c, 2022. "Optimal annuitization post-retirement with labor income," Papers 2202.04220, arXiv.org.
    18. Dadashi, Hassan, 2020. "Optimal investment–consumption problem: Post-retirement with minimum guarantee," Insurance: Mathematics and Economics, Elsevier, vol. 94(C), pages 160-181.
    19. Thomas Bernhardt & Catherine Donnelly, 2019. "Modern tontine with bequest: innovation in pooled annuity products," Papers 1903.05990, arXiv.org.
    20. Francesco Menoncin & Elena Vigna, 2013. "Mean-variance target-based optimisation in DC plan with stochastic interest rate," Carlo Alberto Notebooks 337, Collegio Carlo Alberto.

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