Consumption-Portfolio Choice with Preferences for Cash

43 Pages Posted: 11 Sep 2017 Last revised: 23 Jul 2018

See all articles by Holger Kraft

Holger Kraft

Goethe University Frankfurt

Farina Weiss

Goethe University Frankfurt

Multiple version iconThere are 2 versions of this paper

Date Written: July 12, 2018

Abstract

This paper studies a consumption-portfolio problem where money enters the agent's utility function. We solve the corresponding Hamilton-Jacobi-Bellman equation and provide closed-form solutions for the optimal consumption and portfolio strategy both in an infinite- and finite-horizon setting. For the infinite-horizon problem, the optimal stock demand is one particular root of a polynomial. In the finite-horizon case, the optimal stock demand is given by the inverse of the solution to an ordinary differential equation that can be solved explicitly. We also prove verification results showing that the solution to the Bellman equation is indeed the value function of the problem. From an economic point of view, we find that in the finite-horizon case the optimal stock demand is typically decreasing in age, which is in line with rules of thumb given by financial advisers and also with recent empirical evidence. Our results are robust to introducing recursive utility.

Keywords: consumption-portfolio choice, money in the utility function, stock demand, stochastic control, recursive utility

JEL Classification: G11, C61

Suggested Citation

Kraft, Holger and Weiss, Farina, Consumption-Portfolio Choice with Preferences for Cash (July 12, 2018). SAFE Working Paper No. 181. Available at SSRN: https://ssrn.com/abstract=3034165 or http://dx.doi.org/10.2139/ssrn.3034165

Holger Kraft (Contact Author)

Goethe University Frankfurt ( email )

Faculty of Economics and Business Administration
Theodor-W.-Adorno-Platz 3
Frankfurt am Main, 60323
Germany

Farina Weiss

Goethe University Frankfurt ( email )

Faculty of Economics and Business Administration
Theodor-W.-Adorno-Platz 3
Frankfurt am Main, 60323
Germany

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