Optimal execution in a fractional setting with reinforcement learning

Paper: arXiv 2611.11373

Authors: Matthieu Garcin, Jiang Pu, Thomas Verrier

Abstract

We consider the problem of optimal liquidation with linear market impact, as in the seminal work of Almgren and Chriss, but with an asset driven by a fractional Brownian motion. For $H \neq 1/2$, we observe that the deterministic solution given by Almgren and Chriss is no longer optimal. We develop a strategy to exploit the information induced by the correlation between price increments. The strategy is derived from a policy gradient algorithm, parameterized by a neural network, trained to maximise the CARA utility, for which our method allows for significant improvements.

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 7.0/10
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper presents a highly mathematical approach to optimal execution, extending the Almgren-Chriss framework to fractional Brownian motion. It employs advanced reinforcement learning techniques for empirical validation, demonstrating a strong blend of theoretical depth and practical application. The novelty lies in combining fractional calculus with policy gradient methods for this specific problem.

Research Flowchart

  flowchart TD
    A[Research Goal: Optimal Liquidation with Fractional Brownian Motion] --> B{Problem Formulation: Almgren-Chriss + fBM};
    B --> C[Methodology: Policy Gradient Algorithm with Neural Network];
    C --> D[Data/Inputs: Synthetic fBM Price Paths, Linear Market Impact Model];
    D --> E{Computational Process: Maximize CARA Utility Function};
    E --> F[Key Finding 1: Almgren-Chriss Suboptimality for H != 0.5];
    F --> G[Key Finding 2: Significant Improvements via Policy Gradient Strategy];