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Optimal retirement consumption with a stochastic force of mortality

Author

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  • Huang, Huaxiong
  • Milevsky, Moshe A.
  • Salisbury, Thomas S.
Abstract
We extend the lifecycle model (LCM) of consumption over a random horizon (also known as the Yaari model) to a world in which (i) the force of mortality obeys a diffusion process as opposed to being deterministic, and (ii) consumers can adapt their consumption strategy to new information about their mortality rate (also known as health status) as it becomes available. In particular, we derive the optimal consumption rate and focus on the impact of mortality rate uncertainty versus simple lifetime uncertainty — assuming that the actuarial survival curves are initially identical — in the retirement phase where this risk plays a greater role.

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  • Huang, Huaxiong & Milevsky, Moshe A. & Salisbury, Thomas S., 2012. "Optimal retirement consumption with a stochastic force of mortality," Insurance: Mathematics and Economics, Elsevier, vol. 51(2), pages 282-291.
    • Handle: RePEc:eee:insuma:v:51:y:2012:i:2:p:282-291
    DOI: 10.1016/j.insmatheco.2012.03.013
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    Cited by:

    1. Huang, H. & Milevsky, M.A. & Salisbury, T.S., 2017. "Retirement spending and biological age," Journal of Economic Dynamics and Control, Elsevier, vol. 84(C), pages 58-76.
    2. Blake, David & El Karoui, Nicole & Loisel, Stéphane & MacMinn, Richard, 2018. "Longevity risk and capital markets: The 2015–16 update," Insurance: Mathematics and Economics, Elsevier, vol. 78(C), pages 157-173.
    3. Christoph Hambel & Holger Kraft & Lorenz S. Schendel & Mogens Steffensen, 2017. "Life Insurance Demand Under Health Shock Risk," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 84(4), pages 1171-1202, December.
    4. Hippolyte d’Albis & Emmanuel Thibault, 2018. "Ambiguous life expectancy and the demand for annuities," Theory and Decision, Springer, vol. 85(3), pages 303-319, October.
    5. Ewald, Christian-Oliver & Zhang, Aihua, 2017. "On the effects of changing mortality patterns on investment, labour and consumption under uncertainty," Insurance: Mathematics and Economics, Elsevier, vol. 73(C), pages 105-115.
    6. Post, Thomas & Hanewald, Katja, 2013. "Longevity risk, subjective survival expectations, and individual saving behavior," Journal of Economic Behavior & Organization, Elsevier, vol. 86(C), pages 200-220.
    7. Fischer, Marcel & Jensen, Bjarne Astrup & Koch, Marlene, 2023. "Optimal retirement savings over the life cycle: A deterministic analysis in closed form," Insurance: Mathematics and Economics, Elsevier, vol. 112(C), pages 48-58.
    8. Marcus C. Christiansen, 2013. "Gaussian and Affine Approximation of Stochastic Diffusion Models for Interest and Mortality Rates," Risks, MDPI, vol. 1(3), pages 1-20, October.
    9. Butt, Adam & Khemka, Gaurav & Warren, Geoffrey J., 2022. "Heterogeneity in optimal investment and drawdown strategies in retirement," Pacific-Basin Finance Journal, Elsevier, vol. 74(C).
    10. Feigenbaum, James, 2016. "Equivalent representations of non-exponential discounting models," Journal of Mathematical Economics, Elsevier, vol. 66(C), pages 58-71.
    11. Paolo Guasoni & Yu-Jui Huang, 2019. "Consumption, investment and healthcare with aging," Finance and Stochastics, Springer, vol. 23(2), pages 313-358, April.
    12. Menoncin, Francesco & Regis, Luca, 2017. "Longevity-linked assets and pre-retirement consumption/portfolio decisions," Insurance: Mathematics and Economics, Elsevier, vol. 76(C), pages 75-86.
    13. Schendel, Lorenz S., 2014. "Consumption-investment problems with stochastic mortality risk," SAFE Working Paper Series 43, Leibniz Institute for Financial Research SAFE.
    14. Paweł Rokita & Radosław Pietrzyk & Łukasz Feldman, 2014. "Multiobjective Optimization of Financing Household Goals with Multiple Investment Programs," Statistics in Transition new series, Główny Urząd Statystyczny (Polska), vol. 15(2), pages 243-268, March.
    15. Francesco Menoncin & Luca Regis, 2015. "Longevity assets and pre-retirement consumption/portfolio decisions," Working Papers 2/2015, IMT School for Advanced Studies Lucca, revised May 2015.
    16. Wen Chen & Nicolas Langren'e, 2020. "Deep neural network for optimal retirement consumption in defined contribution pension system," Papers 2007.09911, arXiv.org, revised Jul 2020.
    17. de Kort, J. & Vellekoop, M.H., 2017. "Existence of optimal consumption strategies in markets with longevity risk," Insurance: Mathematics and Economics, Elsevier, vol. 72(C), pages 107-121.
    18. Yang, Qianqian & Ye, Zihan & Chen, Rongda, 2024. "Working longer or working harder? Subjective survival expectations and labor supply in China," International Review of Economics & Finance, Elsevier, vol. 91(C), pages 827-847.
    19. Kraft, Holger & Schendel, Lorenz S. & Steffensen, Mogens, 2014. "Life insurance demand under health shock risk," SAFE Working Paper Series 40, Leibniz Institute for Financial Research SAFE.
    20. Andreas Lichtenstern & Pavel V. Shevchenko & Rudi Zagst, 2019. "Optimal life-cycle consumption and investment decisions under age-dependent risk preferences," Papers 1908.09976, arXiv.org.
    21. Wen Chen & Nicolas Langrené, 2020. "Deep neural network for optimal retirement consumption in defined contribution pension system [Réseau de neurones profond pour consommation à la retraite optimale en système de retraite à cotisatio," Working Papers hal-02909818, HAL.
    22. Paolo Guasoni & Yu-Jui Huang, 2019. "Consumption, Investment, and Healthcare with Aging," Papers 1901.00424, arXiv.org, revised Jan 2019.
    23. Delong, Łukasz & Chen, An, 2016. "Asset allocation, sustainable withdrawal, longevity risk and non-exponential discounting," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 342-352.
    24. Alfredo Omar Palafox-Roca, 2023. "Consumo óptimo en el retiro con diferentes leyes de mortalidad," Remef - Revista Mexicana de Economía y Finanzas Nueva Época REMEF (The Mexican Journal of Economics and Finance), Instituto Mexicano de Ejecutivos de Finanzas, IMEF, vol. 18(3), pages 1-30, Julio - S.
    25. Yassmin Ali & Ming Fang & Pablo A. Arrutia Sota & Stephen Taylor & Xun Wang, 2019. "Social Security Benefit Valuation, Risk, and Optimal Retirement," Risks, MDPI, vol. 7(4), pages 1-31, December.

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