Optimal Dynamic Fees in Automated Market Makers

ArXiv ID: 2506.02869 “View on arXiv”

Authors: Unknown

Abstract

Automated Market Makers (AMMs) are emerging as a popular decentralised trading platform. In this work, we determine the optimal dynamic fees in a constant function market maker. We find approximate closed-form solutions to the control problem and study the optimal fee structure. We find that there are two distinct fee regimes: one in which the AMM imposes higher fees to deter arbitrageurs, and another where fees are lowered to increase volatility and attract noise traders. Our results also show that dynamic fees that are linear in inventory and are sensitive to changes in the external price are a good approximation of the optimal fee structure and thus constitute suitable candidates when designing fees for AMMs.

Keywords: Automated Market Maker (AMM), dynamic fees, constant function market maker, inventory management, arbitrage deterrence, Decentralized Finance (DeFi)

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 6.5/10
• Quadrant: Holy Grail
• Why: The paper formulates and solves complex stochastic control problems with HJB equations and approximate closed-form solutions (high math). It also includes simulations comparing optimal policies to alternatives, validating the theoretical findings against data (moderate-to-high empirical rigor).

  flowchart TD
    A["Research Goal<br>Determine Optimal Dynamic Fees in AMMs"] --> B["Methodology<br>Stochastic Control Problem Formulation"]
    B --> C{"Data/Inputs<br>Market Price Dynamics & Trading Flow"}
    C --> D["Computational Process<br>Approximate Closed-Form Solutions"]
    D --> E{"Findings/Outcomes"}
    
    E --> F["Regime 1: High Fees<br>Deter Arbitrageurs"]
    E --> G["Regime 2: Low Fees<br>Attract Noise Traders"]
    E --> H["Optimal Structure<br>Linear in Inventory & Sensitive to External Price"]