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Mean-variance dynamic portfolio allocation with transaction costs: a Wiener chaos expansion approach

Author

Listed:
  • Areski Cousin

    (IRMA - Institut de Recherche Mathématique Avancée - UNISTRA - Université de Strasbourg - CNRS - Centre National de la Recherche Scientifique)

  • Jérôme Lelong

    (DAO - Données, Apprentissage et Optimisation - LJK - Laboratoire Jean Kuntzmann - Inria - Institut National de Recherche en Informatique et en Automatique - CNRS - Centre National de la Recherche Scientifique - UGA - Université Grenoble Alpes - Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology - UGA - Université Grenoble Alpes, LJK - Laboratoire Jean Kuntzmann - UPMF - Université Pierre Mendès France - Grenoble 2 - UJF - Université Joseph Fourier - Grenoble 1 - Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology - CNRS - Centre National de la Recherche Scientifique)

  • Tom Picard

    (DAO - Données, Apprentissage et Optimisation - LJK - Laboratoire Jean Kuntzmann - Inria - Institut National de Recherche en Informatique et en Automatique - CNRS - Centre National de la Recherche Scientifique - UGA - Université Grenoble Alpes - Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology - UGA - Université Grenoble Alpes)

Abstract

This paper studies the multi-period mean-variance portfolio allocation problem with transaction costs. Many methods have been proposed these last years to challenge the famous uni-period Markowitz strategy. But these methods cannot integrate transaction costs or become computationally heavy and hardly applicable. In this paper, we try to tackle this allocation problem by proposing an innovative approach which relies on representing the set of admissible portfolios by a finite dimensional Wiener chaos expansion. This numerical method is able to find an optimal strategy for the allocation problem subject to transaction costs. To complete the study, the link between optimal portfolios submitted to transaction costs and the underlying risk aversion is investigated. Then a competitive and compliant benchmark based on the sequential uni-period Markowitz strategy is built to highlight the efficiency of our approach.

Suggested Citation

  • Areski Cousin & Jérôme Lelong & Tom Picard, 2024. "Mean-variance dynamic portfolio allocation with transaction costs: a Wiener chaos expansion approach," Post-Print hal-04086378, HAL.
    • Handle: RePEc:hal:journl:hal-04086378
    DOI: 10.1080/1350486X.2024.2357200
    Note: View the original document on HAL open archive server: https://hal.univ-grenoble-alpes.fr/hal-04086378v2
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