Quasi-Hyperbolic Discounting under Recursive Utility and Consumption-Investment Decisions

48 Pages Posted: 27 Sep 2020

Date Written: August 13, 2020

Abstract

This paper examines an Epstein-Zin recursive utility with quasi-hyperbolic discounting in continuous time. I directly define the utility process and consider a Merton's optimal consumption-investment problem for application. I show that a solution to the Hamilton-Jacobi-Bellman equation is the value function. The numerical comparative statics and mathematical analysis shows that, unlike in the constant relative risk aversion utility, present bias in the Epstein-Zin utility causes economically significant overconsumption, maintaining a plausible attitude toward risks. Additionally, I show that the sophisticated agent's preproperation occurs if and only if his or her elasticity of intertemporal substitution in consumption is larger than one.

Keywords: Quasi-Hyperbolic Discounting, Epstein-Zin Utility, Consumption-Investment Problem, Beta-Delta Model, Recursive Utility

JEL Classification: D15, G11, G40

Suggested Citation

Shigeta, Yuki, Quasi-Hyperbolic Discounting under Recursive Utility and Consumption-Investment Decisions (August 13, 2020). Available at SSRN: https://ssrn.com/abstract=3672999 or http://dx.doi.org/10.2139/ssrn.3672999

Yuki Shigeta (Contact Author)

Tokyo Keizai University ( email )

1-7-34, Minami-cho, Kokubunji-shi, Tokyo
Tokyo, 185-8502
Japan

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