Shortermism and excessive risk taking in optimal execution with a target performance

ArXiv ID: 2505.15611 “View on arXiv”

Authors: Emilio Barucci, Yuheng Lan

Abstract

We deal with the optimal execution problem when the broker’s goal is to reach a performance barrier avoiding a downside barrier. The performance is provided by the wealth accumulated by trading in the market, the shares detained by the broker evaluated at the market price plus a slippage cost yielding a quadratic inventory cost. Over a short horizon, this type of remuneration leads, at the same time, to a more aggressive and less risky strategy compared to the classical one, and over a long horizon the performance turns to be poorer and more dispersed.

Keywords: Optimal Execution, Quadratic Inventory Cost, Barrier Constraints, Slippage, High-Frequency Trading, Equities

Complexity vs Empirical Score

• Math Complexity: 9.0/10
• Empirical Rigor: 2.0/10
• Quadrant: Lab Rats
• Why: The paper is mathematically dense, featuring continuous-time stochastic calculus, HJB equations, and closed-form derivations typical of theoretical quantitative finance. It lacks empirical backtests, real-world data, or implementation details, relying solely on analytical solutions and theoretical analysis.

  flowchart TD
    A["Research Goal:<br>Optimal Execution with Performance Barriers"]
    B["Methodology:<br>Dynamic Programming & HJB Equation"]
    C["Inputs:<br>Market Data, Slippage & Inventory Costs"]
    D["Computation:<br>Optimal Strategy via Lagrange Multipliers"]
    E["Outcome 1:<br>Short-term: Aggressive but Low Risk"]
    F["Outcome 2:<br>Long-term: Poorer & Dispersed Performance"]

    A --> B
    B --> C
    C --> D
    D --> E
    D --> F