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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 ISSN 0960-1627.
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Official URL: https://doi.org/10.1111/mafi.12187
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 | ||||||||
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| Subjects: | H Social Sciences > HB Economic Theory | ||||||||
| Divisions: | Faculty of Science, Engineering and Medicine > 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: |
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| Volume: | 29 | ||||||||
| Number: | 2 | ||||||||
| Page Range: | pp. 483-506 | ||||||||
| DOI: | 10.1111/mafi.12187 | ||||||||
| Status: | Peer Reviewed | ||||||||
| Publication Status: | Published | ||||||||
| Reuse Statement (publisher, data, author rights): | "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 | ||||||||
| Date of first compliant deposit: | 30 April 2018 | ||||||||
| Date of first compliant Open Access: | 7 August 2020 | ||||||||
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