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Consumption, Investment, and Healthcare with Aging

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  • Paolo Guasoni
  • Yu-Jui Huang

Abstract

This paper solves the problem of optimal dynamic consumption, investment, and healthcare spending with isoelastic utility, when natural mortality grows exponentially to reflect 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," Papers 1901.00424, arXiv.org, revised Jan 2019.
  • Handle: RePEc:arx:papers:1901.00424
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    File URL: http://arxiv.org/pdf/1901.00424
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    References listed on IDEAS

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    1. Richard, Scott F., 1975. "Optimal consumption, portfolio and life insurance rules for an uncertain lived individual in a continuous time model," Journal of Financial Economics, Elsevier, vol. 2(2), pages 187-203, June.
    2. Ehrlich, Isaac & Chuma, Hiroyuki, 1990. "A Model of the Demand for Longevity and the Value of Life Extension," Journal of Political Economy, University of Chicago Press, vol. 98(4), pages 761-782, August.
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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 Apr 2020.
    2. Joshua Aurand & Yu-Jui Huang, 2019. "Epstein-Zin Utility Maximization on Random Horizons," Papers 1903.08782, arXiv.org, revised Mar 2020.

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