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Consumption, investment and healthcare with aging

Author

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  • Paolo Guasoni

    (Boston University
    Dublin City University)

  • Yu-Jui Huang

    (University of Colorado)

Abstract

This paper solves the problem of optimal dynamic investment, consumption and healthcare spending with isoelastic utility, when natural mortality grows exponentially to reflect the Gompertz law and investment opportunities are constant. Healthcare slows the natural growth of mortality, indirectly increasing utility from consumption through longer lifetimes. Optimal consumption and healthcare imply an endogenous mortality law that is asymptotically exponential in the old-age limit, with lower growth rate than natural mortality. Healthcare spending steadily increases with age, both in absolute terms and relative to total spending. The optimal stochastic control problem reduces to a nonlinear ordinary differential equation with a unique solution, which has an explicit expression in the old-age limit. The main results are obtained through a novel version of Perron’s method.

Suggested Citation

  • Paolo Guasoni & Yu-Jui Huang, 2019. "Consumption, investment and healthcare with aging," Finance and Stochastics, Springer, vol. 23(2), pages 313-358, April.
    • Handle: RePEc:spr:finsto:v:23:y:2019:i:2:d:10.1007_s00780-019-00383-6
    DOI: 10.1007/s00780-019-00383-6
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    Cited by:

    1. Joshua Aurand & Yu-Jui Huang, 2020. "Mortality and Healthcare: a Stochastic Control Analysis under Epstein-Zin Preferences," Papers 2003.01783, arXiv.org, revised Jul 2021.
    2. Joshua Aurand & Yu-Jui Huang, 2019. "Epstein-Zin Utility Maximization on a Random Horizon," Papers 1903.08782, arXiv.org, revised May 2023.
    3. Giorgio Ferrari & Shihao Zhu, 2022. "On a Merton Problem with Irreversible Healthcare Investment," Papers 2212.05317, arXiv.org, revised Dec 2023.
    4. 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

    Healthcare; Consumption–investment; Gompertz’ law; Viscosity solutions; Perron’s method;
    All these keywords.

    JEL classification:

    • E21 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Consumption; Saving; Wealth
    • I12 - Health, Education, and Welfare - - Health - - - Health Behavior

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