A multi-asset investment and consumption problem with transaction costs

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 t...

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Bibliographic Details
Published in:Finance and stochastics 2019-07, Vol.23 (3), p.641-676
Main Authors: Hobson, David, Tse, Alex S. L., Zhu, Yeqi
Format: Article
Language:English
Subjects:
Assets
Boundary value problems
Consumption
Differential equations
Economic models
Economic Theory/Quantitative Economics/Mathematical Methods
Economics
Finance
Ill posed problems
Insurance
Investment
Management
Mathematics
Mathematics and Statistics
Probability Theory and Stochastic Processes
Quadratic equations
Quantitative Finance
Sales
Statistics for Business
Transaction costs
Well posed problems
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Summary: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.
ISSN:0949-2984
1432-1122
DOI:10.1007/s00780-019-00391-6