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Finance and Stochastics

, Volume 23, Issue 4, pp 861–888 | Cite as

Finite-horizon optimal investment with transaction costs: construction of the optimal strategies

  • Christoph BelakEmail author
  • Jörn Sass
Article
  • 23 Downloads

Abstract

We revisit the problem of maximising expected utility of terminal wealth in a Black–Scholes market with proportional transaction costs. While it is known that the value function of this problem is the unique viscosity solution of the HJB equation and that the HJB equation admits a classical solution on a reduced state space, it has been an open problem to verify that these two coincide. We establish this result by devising a verification procedure based on superharmonic functions. In the process, we construct optimal strategies and provide a detailed analysis of the regularity of the value function.

Keywords

Utility maximisation Transaction costs Reflected diffusions Superharmonic functions 

Mathematics Subject Classification (2010)

93E20 35R35 91G80 

JEL Classification

G11 C61 

Notes

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Faculty II – Mathematics and Natural Sciences, Institute of MathematicsTechnische Universität BerlinBerlinGermany
  2. 2.Department of MathematicsUniversity of KaiserslauternKaiserslauternGermany

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