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

ArXiv ID: 2308.02049 “View on arXiv”

Authors: Unknown

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.

Keywords: Portfolio Selection, Hidden Markov Model, Kalman Filter, Dynamic Programming, Mean Reverting Process, Equities

Complexity vs Empirical Score

• Math Complexity: 9.0/10
• Empirical Rigor: 3.0/10
• Quadrant: Lab Rats
• Why: The paper is highly theoretical, involving advanced stochastic calculus (Kalman-Bucy filters, Ornstein-Uhlenbeck processes), dynamic programming, and PIDEs with regularization arguments, but lacks implementation details, backtests, or statistical performance metrics, focusing instead on mathematical existence, uniqueness, and convergence proofs.

  flowchart TD
    A["Research Goal:<br/>Optimal Portfolio Selection with<br/>Hidden Drift & Expert Opinions"] --> B["Key Methodology<br/>Kalman Filter & Dynamic Programming"]
    
    B --> C{"Data & Inputs"}
    C --> D["Hidden Gaussian<br/>Mean-Reverting Drift"]
    C --> E["Noisy Expert<br/>Opinions"]
    C --> F["Poisson Process<br/>Arrival Times"]
    
    D & E & F --> G["Computational Process"]
    G --> H["Estimate State:<br/>Conditional Mean & Covariance"]
    H --> I["Solve Optimization:<br/>Dynamic Programming Equation"]
    
    I --> J["Key Outcomes<br/>Theoretical Results &<br/>Optimal Portfolio Weights"]