EURO 2024 Copenhagen
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3042. Expert Opinions and Power Utility Maximization in a Market with Partially Observable Gaussian Drift

Invited abstract in session MC-57: Dynamic portfolio selection: stochastic optimization, filtering, and learning techniques, stream Modern Decision Making in Finance and Insurance.

Monday, 12:30-14:00
Room: S06 (building: 101)

Authors (first author is the speaker)

1. Ralf Wunderlich
Institute of Mathematics, Brandenburg University of Technology Cottbus-Senftenberg

Abstract

We consider 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 also study diffusion approximations of the filter processes for high-frequency discrete-time experts. They allow to simplify the problem and to derive more explicit solutions. Finally, we illustrate our theoretical findings by results of numerical experiments.

The talk is based on joint work with A. Gabih, H. Kondakji, J. Sass and D. Westphal.

Keywords

Status: accepted

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