A multi-asset investment and consumption problem with transaction costs

David Hobson (), Alex S. L. Tse () and Yeqi Zhu ()
Additional contact information
David Hobson: University of Warwick
Alex S. L. Tse: Imperial College London
Yeqi Zhu: Credit Suisse

Finance and Stochastics, 2019, vol. 23, issue 3, No 5, 676 pages

Abstract: 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.

Keywords: Portfolio choice; Transaction costs; Multiple assets; Hamilton–Jacobi–Bellman equation; Free boundary value problem; 91G10; 93E20 (search for similar items in EconPapers)
JEL-codes: G11 (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (4)

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DOI: 10.1007/s00780-019-00391-6

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