Portfolio Optimization in a Market with Hidden Gaussian Drift and Randomly Arriving Expert Opinions: Modeling and Theoretical Results

TL;DR

This paper develops a mathematical framework for optimal portfolio selection in markets with hidden Gaussian drifts and randomly arriving expert opinions, using filtering and dynamic programming techniques.

Contribution

It introduces a model combining hidden Gaussian mean reversion with random expert signals and provides a rigorous solution to the utility maximization problem.

Findings

Derivation of Kalman filter estimates for the hidden drift.

Formulation of the dynamic programming equation for utility maximization.

Mathematical justification of the regularization approach.

Abstract

This paper investigates the optimal selection of portfolios for power utility maximizing investors in a financial market where stock returns depend on a hidden Gaussian mean reverting drift process. Information on the drift is obtained from returns and expert opinions in the form of noisy signals about the current state of the drift arriving randomly over time. The arrival dates are modeled as the jump times of a homogeneous Poisson process. Applying Kalman filter techniques we derive estimates of the hidden drift which are described by the conditional mean and covariance of the drift given the observations. The utility maximization problem is solved with dynamic programming methods. We derive the associated dynamic programming equation and study regularization arguments for a rigorous mathematical justification.