Growth rate of liquidity provider's wealth in G3Ms

Cheuk Yin Lee, Shen-Ning Tung and Tai-Ho Wang

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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.

Date: 2024-03, Revised 2025-01
New Economics Papers: this item is included in nep-mst
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