A Note on Merton's 'Optimum Consumption and Portfolio Rules in a Continuous-Time Model'

11 Pages Posted: 17 Jan 2008 Last revised: 29 Mar 2014

See all articles by Suresh Sethi

Suresh Sethi

University of Texas at Dallas - Naveen Jindal School of Management

Michael I. Taksar

University of Missouri at Columbia - Department of Mathematics (Deceased) ; State University of New York (SUNY), Stony Brook, College of Engineering and Applied Sciences, Department of Applied Mathematics and Statistics (Deceased)

Abstract

In the paper Optimum Consumption and Portfolio Rules in a continuous-Time Model, by R. C. Merton (J. Econ. Theory 3 (1971), 373-413), solutions obtained in cases when marginal utility at zero consumption is finite are not feasible. While they do satisfy the Hamilton-Jacobi Bellman equations, they do not represent appropriate value functions because the boundary behavior near zero wealth is not satisfactorily dealt with. In this note, we specify the boundary behavior and characterize optimal solutions.

Keywords: Consumption/portfolio problem, investment-consumption problem, dynamic programming, stochastic control, R. C. Merton

JEL Classification: G11, C61

Suggested Citation

Sethi, Suresh and Taksar, Michael I., A Note on Merton's 'Optimum Consumption and Portfolio Rules in a Continuous-Time Model'. Journal of Economic Theory, Vol. 46, No. 2, pp. 395-401, 1988, Available at SSRN: https://ssrn.com/abstract=1084243

Suresh Sethi (Contact Author)

University of Texas at Dallas - Naveen Jindal School of Management ( email )

800 W. Campbell Road, SM30
Richardson, TX 75080-3021
United States

Michael I. Taksar

University of Missouri at Columbia - Department of Mathematics (Deceased)

State University of New York (SUNY), Stony Brook, College of Engineering and Applied Sciences, Department of Applied Mathematics and Statistics (Deceased)

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