Exponential Hedging for the Ornstein-Uhlenbeck Process in the Presence of Linear Price Impact

ArXiv ID: 2509.25472 “View on arXiv”

Authors: Yan Dolinsky

Abstract

In this work we study a continuous time exponential utility maximization problem in the presence of a linear temporary price impact. More precisely, for the case where the risky asset is given by the Ornstein-Uhlenbeck diffusion process we compute the optimal portfolio strategy and the corresponding value. Our method of solution relies on duality, and it is purely probabilistic.

Keywords: exponential utility maximization, price impact, Ornstein-Uhlenbeck process, duality method, probabilistic approach, Equity

Complexity vs Empirical Score

• Math Complexity: 9.0/10
• Empirical Rigor: 1.0/10
• Quadrant: Lab Rats
• Why: The paper presents a highly theoretical, continuous-time stochastic control solution using advanced probability, duality, and PDE-like variational methods, with no empirical data, backtesting, or implementation details.

  flowchart TD
    A["Research Goal<br>Exponential Utility Max<br>with Linear Price Impact"] --> B["Key Methodology<br>Duality Method &<br>Probabilistic Approach"]
    B --> C["Data/Inputs<br>Ornstein-Uhlenbeck Process<br>Linear Temporary Impact"]
    C --> D["Computational Process<br>Solve HJB Equation &<br>Compute Optimal Portfolio"]
    D --> E["Key Findings/Outcomes<br>Explicit Optimal Strategy<br>Value Function"]