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Bayesian learning for the Markowitz portfolio selection problem

Author

Listed:
  • Carmine De Franco

    (LPSM UMR 8001)

  • Johann Nicolle

    (LPSM UMR 8001)

  • Huy^en Pham

    (LPSM UMR 8001, CREST)

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 & Huy^en Pham, 2018. "Bayesian learning for the Markowitz portfolio selection problem," Papers 1811.06893, arXiv.org.
    • Handle: RePEc:arx:papers:1811.06893
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    References listed on IDEAS

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    Cited by:

    1. Shubhangi Sikaria & Rituparna Sen & Neelesh S. Upadhye, 2019. "Bayesian Filtering for Multi-period Mean-Variance Portfolio Selection," Papers 1911.07526, arXiv.org, revised Aug 2020.
    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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