Power Utility Maximization with Expert Opinions at Fixed Arrival Times in a Market with Hidden Gaussian Drift

TL;DR

This paper develops a framework for optimal trading in markets with hidden Gaussian drifts, incorporating expert opinions arriving at fixed times, and provides explicit solutions and numerical insights into the value of such information.

Contribution

It introduces a method to incorporate fixed-time expert signals into power utility maximization with hidden Gaussian drifts, deriving explicit solutions and quantifying information value.

Findings

Explicit formulas for the value function and optimal strategy.

Quantification of the monetary value of expert opinions.

Numerical experiments illustrating theoretical results.

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.