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Power utility maximization with expert opinions at fixed arrival times in a market with hidden Gaussian drift

Author

Listed:
  • Abdelali Gabih

    (Equipe de Modélisation et Contrôle des Systèmes Stochastiques et Déterministes, Faculty of Sciences, Chouaib Doukkali University)

  • Hakam Kondakji

    (Helmut Schmidt University)

  • Ralf Wunderlich

    (Brandenburg University of Technology Cottbus-Senftenberg)

Abstract

In this paper we study optimal trading strategies in a financial market in which stock returns depend on a hidden Gaussian mean reverting drift process. Investors obtain information on that drift by observing stock returns. Moreover, expert opinions in the form of signals about the current state of the drift arriving at fixed and known dates are included in the analysis. Drift estimates are based on Kalman filter techniques. They are used to transform a power utility maximization problem under partial information into an optimization problem under full information where the state variable is the filter of the drift. The dynamic programming equation for this problem is studied and closed-form solutions for the value function and the optimal trading strategy of an investor are derived. They allow to quantify the monetary value of information delivered by the expert opinions. We illustrate our theoretical findings by results of extensive numerical experiments.

Suggested Citation

  • Abdelali Gabih & Hakam Kondakji & Ralf Wunderlich, 2024. "Power utility maximization with expert opinions at fixed arrival times in a market with hidden Gaussian drift," Annals of Operations Research, Springer, vol. 341(2), pages 897-936, October.
    • Handle: RePEc:spr:annopr:v:341:y:2024:i:2:d:10.1007_s10479-024-06172-5
    DOI: 10.1007/s10479-024-06172-5
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    References listed on IDEAS

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    1. Rudiger Frey & Abdelali Gabih & Ralf Wunderlich, 2013. "Portfolio Optimization under Partial Information with Expert Opinions: a Dynamic Programming Approach," Papers 1303.2513, arXiv.org, revised Feb 2014.
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    5. Abdelali Gabih & Hakam Kondakji & Ralf Wunderlich, 2022. "Well Posedness of Utility Maximization Problems Under Partial Information in a Market with Gaussian Drift," Papers 2205.08614, arXiv.org, revised Jul 2024.
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    9. Abdelali Gabih & Ralf Wunderlich, 2023. "Portfolio Optimization in a Market with Hidden Gaussian Drift and Randomly Arriving Expert Opinions: Modeling and Theoretical Results," Papers 2308.02049, arXiv.org, revised Jun 2024.
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    18. Abdelali Gabih & Hakam Kondakji & Jorn Sass & Ralf Wunderlich, 2014. "Expert Opinions and Logarithmic Utility Maximization in a Market with Gaussian Drift," Papers 1402.6313, arXiv.org.
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