A Note on Optimal Liquidation with Linear Price Impact

ArXiv ID: 2402.14100 “View on arXiv”

Authors: Unknown

Abstract

In this note we consider the maximization of the expected terminal wealth for the setup of quadratic transaction costs. First, we provide a very simple probabilistic solution to the problem. Although the problem was largely studied, as far as we know up to date this simple and probabilistic form of the solution has not appeared in the literature. Next, we apply the general result for the numerical study of the case where the risky asset is given by a fractional Brownian Motion and the information flow of the investor can be diversified.

Keywords: Portfolio Optimization, Transaction Costs, Fractional Brownian Motion, Stochastic Control, Optimal Execution

Complexity vs Empirical Score

• Math Complexity: 9.5/10
• Empirical Rigor: 2.0/10
• Quadrant: Lab Rats
• Why: The paper presents a highly theoretical solution using advanced stochastic calculus and martingale theory without any real-world data or backtesting, focusing on a mathematical derivation for an idealized liquidation model.

  flowchart TD
    A["Research Goal<br>Maximize expected terminal wealth<br>with quadratic transaction costs"] --> B{"Methodology"}
    
    B --> C["Probabilistic Solution Derivation<br>Mathematical derivation for general case"]
    B --> D["Numerical Application<br>Apply to Fractional Brownian Motion<br>with diversified information flow"]
    
    C --> E["Key Findings<br>1. Simple probabilistic form<br>2. Novel result in literature"]
    D --> F["Key Findings<br>1. Application framework established<br>2. Numerical implementation ready"]
    
    E --> G["Outcomes<br>Contribution to Portfolio Optimization<br>and Optimal Execution Theory"]
    F --> G
    
    style A fill:#e1f5fe
    style G fill:#f3e5f5