Paper: arXiv 2502.07868

Abstract

This paper studies the ubiquitous problem of liquidating large quantities of highly correlated stocks, a task frequently encountered by institutional investors and proprietary trading firms. Traditional methods in this setting suffer from the curse of dimensionality, making them impractical for high-dimensional problems. In this work, we propose a novel method based on stochastic optimal control to optimally tackle this complex multidimensional problem. The proposed method minimizes the overall execution shortfall of highly correlated stocks using a reinforcement learning approach. We rigorously establish the convergence of our optimal trading strategy and present an implementation of our algorithm using intra-day market data.

Complexity vs Empirical Score

  • Math Complexity: 7.5/10
  • Empirical Rigor: 6.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper applies advanced stochastic optimal control and reinforcement learning with multiple mathematical proofs and derivations, indicating high math complexity. It includes real intra-day market data implementation and a GitHub repository with code, demonstrating substantial empirical rigor.

Research Flowchart

  flowchart TD
  A["Research Goal:<br>Liquidation of Correlated Stocks"] --> B["Formulate as<br>Stochastic Optimal Control"]
  B --> C["Methodology:<br>Reinforcement Learning"]
  C --> D["Data:<br>Intra-day Market Data"]
  D --> E["Computational Process:<br>RL Algorithm Implementation"]
  E --> F["Key Findings:<br>Minimal Shortfall Strategy"]
  F --> G["Outcome:<br>Convergent & Optimal Execution"]