Finance and Stochastics

, Volume 23, Issue 1, pp 29–96 | Cite as

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

  • Christoph BelakEmail author
  • Sören Christensen


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.


Portfolio optimisation Transaction costs Discontinuous viscosity solutions Comparison principle Stochastic Perron method 

Mathematics Subject Classification (2010)

93E20 49L25 91G80 

JEL Classification

G11 C61 



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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department IVUniversity of TrierTrierGermany
  2. 2.Department of Mathematics, SPSTUniversity of HamburgHamburgGermany

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