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Bayesian learning for the Markowitz portfolio selection problem

Author

Listed:
  • Carmine de Franco

    (OSSIAM)

  • Johann Nicolle

    (LPSM (UMR_8001) - Laboratoire de Probabilités, Statistique et Modélisation - UPD7 - Université Paris Diderot - Paris 7 - SU - Sorbonne Université - CNRS - Centre National de la Recherche Scientifique, OSSIAM)

  • Huyên Pham

    (LPSM (UMR_8001) - Laboratoire de Probabilités, Statistique et Modélisation - UPD7 - Université Paris Diderot - Paris 7 - SU - Sorbonne Université - CNRS - Centre National de la Recherche Scientifique, CREST - Centre de Recherche en Economie et en Statistique - ENSAE Paris - École Nationale de la Statistique et de l'Administration Économique)

Abstract

We study the Markowitz portfolio selection problem with unknown drift vector in the multidimensional framework. The prior belief on the uncertain expected rate of return is modeled by an arbitrary probability law, and a Bayesian approach from filtering theory is used to learn the posterior distribution about the drift given the observed market data of the assets. The Bayesian Markowitz problem is then embedded into an auxiliary standard control problem that we characterize by a dynamic programming method and prove the existence and uniqueness of a smooth solution to the related semi-linear partial differential equation (PDE). The optimal Markowitz portfolio strategy is explicitly computed in the case of a Gaussian prior distribution. Finally, we measure the quantitative impact of learning, updating the strategy from observed data, compared to non-learning, using a constant drift in an uncertain context, and analyze the sensitivity of the value of information w.r.t. various relevant parameters of our model.

Suggested Citation

  • Carmine de Franco & Johann Nicolle & Huyên Pham, 2018. "Bayesian learning for the Markowitz portfolio selection problem," Working Papers hal-01923917, HAL.
    • Handle: RePEc:hal:wpaper:hal-01923917
    DOI: 10.1142/S0219024919500377
    Note: View the original document on HAL open archive server: https://hal.science/hal-01923917v1
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    References listed on IDEAS

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    Cited by:

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    2. Trichilli, Yousra & Abbes, Mouna Boujelbène & Masmoudi, Afif, 2020. "Islamic and conventional portfolios optimization under investor sentiment states: Bayesian vs Markowitz portfolio analysis," Research in International Business and Finance, Elsevier, vol. 51(C).

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