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A geometric approach to portfolio optimization in models with transaction costs

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Abstract.

We consider a continuous-time stochastic optimization problem with infinite horizon, linear dynamics, and cone constraints which includes as a particular case portfolio selection problems under transaction costs for models of stock and currency markets. Using an appropriate geometric formalism we show that the Bellman function is the unique viscosity solution of a HJB equation.

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Authors and Affiliations

  1. Université de Franche-Comté, 16 Route de Gray, 25030, Besançon Cedex, France

    Yuri Kabanov

  2. Central Economics and Mathematics Institute, Moscow, Russia

    Yuri Kabanov

  3. Center for Mathematical Sciences, Munich University of Technology, Boltzmannstrasse 3, 85747, Garching bei München, Germany

    Claudia Klüppelberg

Authors
  1. Yuri Kabanov
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  2. Claudia Klüppelberg
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Corresponding author

Correspondence to Yuri Kabanov.

Additional information

Mathematics Subject Classification (1991):

60G44

JEL Classification:

G13, G11

This research was done at Munich University of Technology supported by a Mercator Guest Professorship of the German Science Foundation (Deutsche Forschungsgemeinschaft). The authors also express their thanks to Mark Davis, Steve Shreve, and Michael Taksar for useful discussions concerning the principle of dynamic programming.

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Kabanov, Y., Klüppelberg, C. A geometric approach to portfolio optimization in models with transaction costs. Finance and Stochastics 8, 207–227 (2004). https://doi.org/10.1007/s00780-003-0114-3

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  • DOI: https://doi.org/10.1007/s00780-003-0114-3

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