Utility maximisation in a factor model with constant and proportional transaction costs

Christoph Belak () and Sören Christensen ()
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Christoph Belak: University of Trier
Sören Christensen: University of Hamburg

Finance and Stochastics, 2019, vol. 23, issue 1, No 2, 29-96

Abstract: Abstract We study the problem of maximising expected utility of terminal wealth under constant and proportional transaction costs in a multidimensional market with prices driven by a factor process. We show that the value function is the unique viscosity solution of the associated quasi-variational inequalities and construct optimal strategies. While the value function turns out to be truly discontinuous, we are able to establish a comparison principle for discontinuous viscosity solutions which is strong enough to argue that the value function is unique, globally upper semicontinuous, and continuous if restricted to either borrowing or non-borrowing portfolios.

Keywords: Portfolio optimisation; Transaction costs; Discontinuous viscosity solutions; Comparison principle; Stochastic Perron method; 93E20; 49L25; 91G80 (search for similar items in EconPapers)
JEL-codes: C61 G11 (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (7)

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DOI: 10.1007/s00780-018-00380-1

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