Mathematical Methods of Operations Research

, Volume 77, Issue 1, pp 101–130 | Cite as

Primal-dual methods for the computation of trading regions under proportional transaction costs

  • Roland HerzogEmail author
  • Karl Kunisch
  • Jörn Sass
Original Article


Portfolio optimization problems on a finite time horizon under proportional transaction costs are considered. The objective is to maximize the expected utility of the terminal wealth. The ensuing non-smooth time-dependent Hamilton–Jacobi–Bellman equation is solved by regularization and the application of a semi-smooth Newton method. Discretization in space is carried out by finite differences or finite elements. Computational results for one and two risky assets are provided.


Portfolio optimization Transaction costs Complementarity problem Semi-smooth Newton method Augmented Lagrangian method 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Faculty of MathematicsChemnitz University of TechnologyChemnitzGermany
  2. 2.Institute for Mathematics and Scientific ComputingKarl Franzens University GrazGrazAustria
  3. 3.Department of MathemaicsUniversity of KaiserslauternKaiserslauternGermany

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