Growth rate of liquidity provider’s wealth in G3Ms

ArXiv ID: 2403.18177 “View on arXiv”

Authors: Unknown

Abstract

We study how trading fees and continuous-time arbitrage affect the profitability of liquidity providers (LPs) in Geometric Mean Market Makers (G3Ms). We use stochastic reflected diffusion processes to analyze the dynamics of a G3M model under the arbitrage-driven market. Our research focuses on calculating LP wealth and extends the findings of Tassy and White related to the constant product market maker (Uniswap v2) to a wider range of G3Ms, including Balancer. This allows us to calculate the long-term expected logarithmic growth of LP wealth, offering new insights into the complex dynamics of AMMs and their implications for LPs in decentralized finance.

Keywords: Geometric Mean Market Maker, Liquidity Providers, Stochastic Reflected Diffusion, LP Wealth, Arbitrage, Cryptocurrency/DeFi

Complexity vs Empirical Score

• Math Complexity: 9.0/10
• Empirical Rigor: 2.0/10
• Quadrant: Lab Rats
• Why: The paper is heavily mathematical, utilizing stochastic calculus, reflected diffusion processes, and deriving explicit formulas via parabolic PDEs with Neumann boundary conditions, placing it at the high end of complexity. However, it lacks any empirical validation, backtests, or implementation details, focusing purely on theoretical analysis and model derivation.

  flowchart TD
    A["Research Goal: Analyze LP Wealth Growth<br>in Geometric Mean Market Makers"] --> B["Key Methodology: Stochastic<br>Reflected Diffusion Processes"]
    B --> C["Data: Arbitrage-Driven Market<br>Trading Fee Structures"]
    C --> D{"Computational Process"}
    D --> E["Model G3M Dynamics<br>Under Arbitrage"]
    D --> F["Extend Tassy & White Findings<br>to Balancer & G3Ms"]
    E --> G["Calculate Long-Term<br>Expected Logarithmic Growth"]
    F --> G
    G --> H["Key Outcomes: New Insights on<br>LP Profitability & AMM Dynamics"]