Paper: arXiv 2611.14245

Authors: Ryan Donnelly, Luca Galimberti, Brian Healy, Siqi Zhang

Abstract

We analyze the solution map of a optimal execution problem in which price dynamics are subject to a general transient impact kernel. Given the structure of the optimal trading strategy derived by Abi Jaber and Neuman in \cite{https://doi.org/10.1111/mafi.12465}, we show that the strategy is locally Lipschitz continuous with respect to the underlying model parameters governing temporary and transient price impact as well as the fundamental price process. Continuity of this map justifies the application of neural-net based approximations which take model parameters as inputs. We propose a method generating samples of the transient price impact kernel for the purposes of creating training data, and a method of projecting the kernel to a finite dimensional representation appropriate for input to a neural net, and a dimensional reduction based on the relationship between inventory and trade signal. We demonstrate the effectiveness of the trained neural net and use it to quantify the potential financial costs associated with misspecifying the transient impact kernel.

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 rigorous mathematical analysis of optimal liquidation strategies, demonstrating Lipschitz continuity to justify neural network application. It then empirically validates the deep learning approach and quantifies misspecification costs, blending strong theoretical foundations with practical application. The novelty lies in using operator maps with deep learning for general transient impact kernels.

Research Flowchart

  flowchart TD
    A[Research Goal: Approximate Optimal Trading Strategy for Transient Impact] --> B{Analyze Optimal Trading Strategy Structure};
    B --> C[Key Property: Strategy is Locally Lipschitz Continuous w.r.t. Model Parameters];
    C --> D{Methodology: Apply Neural Network Approximation};
    D --> E[Data Generation: Sample Transient Impact Kernels; Finite-Dimensional Kernel Projection];
    E --> F[Computational Process: Train Neural Net; Dimensional Reduction (Inventory-Trade Signal)];
    F --> G[Outcomes: Effective Neural Net Approximation; Quantify Financial Costs of Kernel Misspecification];