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A multi-asset investment and consumption problem with transaction costs

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Title: A multi-asset investment and consumption problem with transaction costs
Authors: Hobson, D
Tse, ASL
Zhu, Y
Item Type: Journal Article
Abstract: In this article, we study a multi-asset version of the Merton investment and consumption problem with CRRA utility and proportional transaction costs. We specialise to a case where transaction costs are zero except for sales and purchases of a single asset which we call the illiquid asset. We show that the underlying HJB equation can be transformed into a boundary value problem for a first order differential equation. Important properties of the multi-asset problem (including when the problem is well-posed, ill-posed, or well-posed for some values of transaction costs only) can be inferred from the behaviours of a quadratic function of a single variable and another algebraic function.
Issue Date: 1-Jan-2019
Date of Acceptance: 5-Mar-2019
URI: http://hdl.handle.net/10044/1/70786
DOI: https://dx.doi.org/10.1007/s00780-019-00391-6
ISSN: 0949-2984
Start Page: 641
End Page: 676
Journal / Book Title: Finance and Stochastics
Volume: 23
Issue: 3
Copyright Statement: © 2019 The Author(s). Open Access. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Keywords: 0102 Applied Mathematics
0104 Statistics
Publication Status: Published
Online Publication Date: 2019-05-28
Appears in Collections:Financial Mathematics
Faculty of Natural Sciences