Consumption, Investment, and Healthcare with Aging

Paolo Guasoni and Yu-Jui Huang

Papers from arXiv.org

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.

Date: 2019-01, Revised 2019-01
New Economics Papers: this item is included in nep-age, nep-hea and nep-upt
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Citations: View citations in EconPapers (6)

Published in Finance and Stochastics, Vol. 23 (2019), Issue 2, pp 313-358

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Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:1901.00424

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