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

Abdelali Gabih (), Hakam Kondakji () and Ralf Wunderlich ()
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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

Annals of Operations Research, 2024, vol. 341, issue 2, No 6, 897-936

Abstract: 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.

Keywords: Power utility maximization; Partial information; Stochastic optimal control; Kalman-Bucy filter; Expert opinions; Black-Litterman model; 91G10; 93E20; 93E11; 60G35 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10479-024-06172-5

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