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

2025-09-29

AI Summary

This paper addresses the continuous-time exponential utility maximization problem for an Ornstein–Uhlenbeck-type mean-reverting asset subject to linear temporary price impact. In the context of an incomplete market—where explicit solutions are generally intractable—the authors develop, for the first time, a rigorous and feasible dual framework by synergistically integrating duality theory with a purely probabilistic approach. This yields closed-form expressions for both the optimal investment strategy and the value function, thereby enabling an analytical characterization of dynamic hedging under price impact. The method overcomes the limitations of conventional deterministic control or asymptotic expansion techniques. It delivers the first explicitly computable, economically interpretable optimal trading strategy for mean-reverting assets in the presence of market frictions. Consequently, it significantly extends the applicability of duality methods to non-Markovian settings with nonlinear transaction costs.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Reasoning under Uncertainty: Decision/Utility Theory
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization

Application Category

• Economics, Online Markets and Human Computation: Sustainability of Web economics
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

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.

Problem

• Exponential utility maximization with linear price impact
• Optimal portfolio strategy for Ornstein-Uhlenbeck process
• Duality method for solving continuous-time investment problem

Innovation

• Exponential utility maximization with linear price impact
• Duality method for Ornstein-Uhlenbeck process optimization
• Probabilistic approach to compute optimal portfolio strategy