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Optimal timing for annuitization, based on jump diffusion fund and stochastic mortality

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  • Hainaut, Donatien
  • Deelstra, Griselda

Abstract

Optimal timing for annuitization is developed along three approaches. Firstly, the mutual fund in which the individual invests before annuitization is modeled by a jump diffusion process. Secondly, instead of maximizing an economic utility, the stopping time is used to maximize the market value of future cash-flows. Thirdly, a solution is proposed in terms of Expected Present Value operators: this shows that the non-annuitization (or continuation) region is either delimited by a lower or upper boundary, in the domain time-assets return. The necessary conditions are given under which these mutually exclusive boundaries exist. Further, a method is proposed to compute the probability of annuitization. Finally, a case study is presented where the mutual fund is fitted to the S&P500 and mortality is modeled by a Gompertz Makeham law with several real scenarios being discussed.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:dyncon:v:44:y:2014:i:c:p:124-146
    DOI: 10.1016/j.jedc.2014.04.008
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    References listed on IDEAS

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    1. 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.
    2. S. G. Kou & Hui Wang, 2004. "Option Pricing Under a Double Exponential Jump Diffusion Model," Management Science, INFORMS, vol. 50(9), pages 1178-1192, September.
    3. Menahem E. Yaari, 1965. "Uncertain Lifetime, Life Insurance, and the Theory of the Consumer," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 32(2), pages 137-150.
    4. Svetlana Boyarchenko & Sergei Levendorskii, 2007. "Irreversible Decisions under Uncertainty," Studies in Economic Theory, Springer, number 978-3-540-73746-9, March.
    5. Huang, H. & Milevsky, M.A. & Salisbury, T.S., 2014. "Optimal initiation of a GLWB in a variable annuity: No Arbitrage approach," Insurance: Mathematics and Economics, Elsevier, vol. 56(C), pages 102-111.
    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. Marina Di Giacinto & Elena Vigna, 2012. "On the sub-optimality cost of immediate annuitization in DC pension funds," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 20(3), pages 497-527, September.
    8. Paul Emms & Steven Haberman, 2008. "Income Drawdown Schemes for a Defined‐Contribution Pension Plan," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 75(3), pages 739-761, September.
    9. Hainaut, Donatien & Devolder, Pierre, 2006. "Life Annuitization: Why and how Much?," ASTIN Bulletin, Cambridge University Press, vol. 36(2), pages 629-654, November.
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    Cited by:

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    2. Tiziano Angelis & Gabriele Stabile, 2019. "On the free boundary of an annuity purchase," Finance and Stochastics, Springer, vol. 23(1), pages 97-137, January.
    3. Hainaut, Donatien, 2015. "Evaluation and default time for companies with uncertain cash flows," Insurance: Mathematics and Economics, Elsevier, vol. 61(C), pages 276-285.
    4. 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.
    5. Li, Han & Liu, Haibo & Tang, Qihe & Yuan, Zhongyi, 2023. "Pricing extreme mortality risk in the wake of the COVID-19 pandemic," Insurance: Mathematics and Economics, Elsevier, vol. 108(C), pages 84-106.
    6. F. Habib & H. Huang & A. Mauskopf & B. Nikolic & T. S. Salisbury, 2021. "Optimal allocation to deferred income annuities," Papers 2111.01234, arXiv.org.
    7. Hassan Dadashi, 2018. "Optimal investment-consumption problem: post-retirement with minimum guarantee," Papers 1803.00611, arXiv.org, revised Aug 2020.
    8. Dadashi, Hassan, 2020. "Optimal investment–consumption problem: Post-retirement with minimum guarantee," Insurance: Mathematics and Economics, Elsevier, vol. 94(C), pages 160-181.
    9. Habib, F. & Huang, H. & Mauskopf, A. & Nikolic, B. & Salisbury, T.S., 2020. "Optimal allocation to Deferred Income Annuities," Insurance: Mathematics and Economics, Elsevier, vol. 90(C), pages 94-104.
    10. Charles I. Nkeki, 2017. "Optimal Investment And Optimal Additional Voluntary Contribution Rate Of A Dc Pension Fund In A Jump-Diffusion Environment," Annals of Financial Economics (AFE), World Scientific Publishing Co. Pte. Ltd., vol. 12(04), pages 1-26, December.

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    More about this item

    Keywords

    Annuity puzzle; Hitting time; Wiener–Hopf factorization; Expected present value;
    All these keywords.

    JEL classification:

    • J26 - Labor and Demographic Economics - - Demand and Supply of Labor - - - Retirement; Retirement Policies
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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