Paper: arXiv 2403.18177

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.

Complexity vs Empirical Score

  • Math Complexity: 9.0/10
  • Empirical Rigor: 2.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: 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.

Research Flowchart

  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"]

Cited References (46)

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  7. Automated Market Making and Loss-Versus-Rebalancing (2022) — link
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and 38 more
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  2. Growth rate of a liquidity provider’s wealth in $xy=c$ automated market makers (2020)
  3. An arbitrage driven price dynamics of Automated Market Makers in the presence of fees — → 2401.01526
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1 of 46 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.