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On the free boundary of an annuity purchase

Author

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  • Tiziano Angelis

    (University of Leeds)

  • Gabriele Stabile

    (Sapienza-Università di Roma)

Abstract

It is known that the decision to purchase an annuity may be associated to an optimal stopping problem. However, little is known about optimal strategies if the mortality force is a generic function of time and the subjective life expectancy of the investor differs from the objective one adopted by insurance companies to price annuities. In this paper, we address this problem by considering an individual who invests in a fund and has the option to convert the fund’s value into an annuity at any time. We formulate the problem as a real option and perform a detailed probabilistic study of the optimal stopping boundary. Due to the generic time-dependence of the mortality force, our optimal stopping problem requires new solution methods to deal with nonmonotonic optimal boundaries.

Suggested Citation

  • Tiziano Angelis & Gabriele Stabile, 2019. "On the free boundary of an annuity purchase," Finance and Stochastics, Springer, vol. 23(1), pages 97-137, January.
    • Handle: RePEc:spr:finsto:v:23:y:2019:i:1:d:10.1007_s00780-018-00379-8
    DOI: 10.1007/s00780-018-00379-8
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    References listed on IDEAS

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    9. Tiziano De Angelis & Erik Ekstrom, 2016. "The dividend problem with a finite horizon," Papers 1609.01655, arXiv.org, revised Nov 2017.
    10. 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.
    11. Goran Peskir, 2005. "On The American Option Problem," Mathematical Finance, Wiley Blackwell, vol. 15(1), pages 169-181, January.
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    Cited by:

    1. Zhenya Liu & Yuhao Mu, 2022. "Optimal Stopping Methods for Investment Decisions: A Literature Review," IJFS, MDPI, vol. 10(4), pages 1-23, October.
    2. Tiziano De Angelis & Alessandro Milazzo & Gabriele Stabile, 2024. "On variable annuities with surrender charges," Papers 2405.02115, arXiv.org.
    3. 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.
    4. Giorgio Ferrari & Shihao Zhu, 2022. "On a Merton Problem with Irreversible Healthcare Investment," Papers 2212.05317, arXiv.org, revised Dec 2023.
    5. Ferrari, Giorgio & Zhu, Shihao, 2023. "Optimal Retirement Choice under Age-dependent Force of Mortality," Center for Mathematical Economics Working Papers 683, Center for Mathematical Economics, Bielefeld University.
    6. Giorgio Ferrari & Shihao Zhu, 2023. "Optimal Retirement Choice under Age-dependent Force of Mortality," Papers 2311.12169, arXiv.org.
    7. 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.
    8. Maria B. Chiarolla & Tiziano Angelis & Gabriele Stabile, 2022. "An analytical study of participating policies with minimum rate guarantee and surrender option," Finance and Stochastics, Springer, vol. 26(2), pages 173-216, April.
    9. Ferrari, Giorgio & Zhu, Shihao, 2022. "Consumption Descision, Portfolio Choice and Healthcare Irreversible Investment," Center for Mathematical Economics Working Papers 671, Center for Mathematical Economics, Bielefeld University.

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    More about this item

    Keywords

    Annuities; Mortality force; Optimal stopping; Free boundary problems;
    All these keywords.

    JEL classification:

    • J26 - Labor and Demographic Economics - - Demand and Supply of Labor - - - Retirement; Retirement Policies

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