Growth rate of liquidity provider's wealth in G3Ms

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 [Milionis et al. 2022a. “Automated Market Making and Loss-Versus-Rebalancing.” arXiv e-prints]. Our research focuses on calculating LP wealth and extends the findings of Tassy and White [Tassy and White. 2020. “Growth Rate of a Liquidity Provider's Wealth in xy = c Automated Market Makers.”] for the constant product market maker (Uniswap v2) to a broader 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.