Optimal Trading in Automated Market Makers with Deep Learning

Paper: arXiv 2304.02180

Authors: Sebastian Jaimungal, Yuri F. Saporito, Max O. Souza, Yuri Thamsten

Abstract

This article explores the optimisation of trading strategies in Constant Function Market Makers (CFMMs) and centralised exchanges. We develop a model that accounts for the interaction between these two markets, estimating the conditional dependence between variables using the concept of conditional elicitability. Furthermore, we pose an optimal execution problem where the agent hides their orders by controlling the rate at which they trade. We do so without approximating the market dynamics. The resulting dynamic programming equation is not analytically tractable, therefore, we employ the deep Galerkin method to solve it. Finally, we conduct numerical experiments and illustrate that the optimal strategy is not prone to price slippage and outperforms naïve strategies.

Complexity vs Empirical Score

• Math Complexity: 8.0/10
• Empirical Rigor: 4.5/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents a sophisticated theoretical framework combining conditional elicitability, stochastic control, and the Deep Galerkin Method to address optimal execution across AMMs and CEXs. While mathematically rigorous and highly novel in its application to DeFi market microstructure, it relies primarily on numerical simulations rather than extensive empirical backtesting with historical dataset validation.

Research Flowchart

  flowchart TD
    A[Research Goal: Optimal Trading Strategy in CFMMs & Centralised Exchanges] --> B[Model Formulation: Joint Market Dynamics & Order Hiding]
    B --> C[Inputs: Conditional Dependence via Conditional Elicitability]
    C --> D[Dynamic Programming Equation: Unapproximated Market Dynamics]
    D --> E[Computation: Deep Galerkin Method Solver]
    E --> F[Numerical Experiments]
    F --> G[Outcomes: Strategy Outperforms Naïve Approaches & Resists Price Slippage]