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Optimal consumption and investment under transaction costs

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Hobson, David G., Tse, Alex Sing-Lam and Zhu, Yeqi (2019) Optimal consumption and investment under transaction costs. Mathematical Finance, 29 (2). pp. 483-506. doi:10.1111/mafi.12187

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Official URL: https://doi.org/10.1111/mafi.12187

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Abstract

In this paper, we consider the Merton problem in a market with a single risky asset and proportional transaction costs. We give a complete solution of the problem up to the solution of a first‐crossing problem for a first‐order differential equation. We find that the characteristics of the solution (e.g., well‐posedness) can be related to some simple properties of a univariate quadratic whose coefficients are functions of the parameters of the problem. Our solution to the problem via the value function includes expressions for the boundaries of the no‐transaction wedge. Using these expressions, we prove a precise condition for when leverage occurs. One new and unexpected result is that when the solution to the Merton problem (without transaction costs) involves a leveraged position, and when transaction costs are large, the location of the boundary at which sales of the risky asset occur is independent of the transaction cost on purchases.

Item Type: Journal Article
Subjects: H Social Sciences > HB Economic Theory
Divisions: Faculty of Science > Statistics
Library of Congress Subject Headings (LCSH): Consumption (Economics), Saving and investment, Transaction costs
Journal or Publication Title: Mathematical Finance
Publisher: Wiley-Blackwell Publishing, Inc.
ISSN: 0960-1627
Official Date: April 2019
Dates:
DateEvent
April 2019Published
7 August 2018Available
12 April 2018Accepted
Volume: 29
Number: 2
Page Range: pp. 483-506
DOI: 10.1111/mafi.12187
Status: Peer Reviewed
Publication Status: Published
Publisher Statement: "This is the peer reviewed version of the following article: Hobson, D, Tse, ASL, Zhu, Y. Optimal consumption and investment under transaction costs. Mathematical Finance. 2019; 29: 483– 506. https://doi.org/10.1111/mafi.12187. which has been published in final form at https://doi.org/10.1111/mafi.12187. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions."
Access rights to Published version: Restricted or Subscription Access
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