Hobson, D;
Tse, ASL;
Zhu, Y;
(2019)
A multi-asset investment and consumption problem with transaction costs.
Finance and Stochastics
, 23
pp. 641-676.
10.1007/s00780-019-00391-6.
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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.
| Type: | Article |
|---|---|
| Title: | A multi-asset investment and consumption problem with transaction costs |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1007/s00780-019-00391-6 |
| Publisher version: | https://doi.org/10.1007/s00780-019-00391-6 |
| Language: | English |
| Additional information: | 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: | Portfolio choice, Transaction costs, Multiple assets, Hamilton–Jacobi–Bellman equation, Free boundary value problem |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10137465 |
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