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Growth rate of liquidity provider's wealth in G3Ms

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  • Cheuk Yin Lee
  • Shen-Ning Tung
  • Tai-Ho Wang

Abstract

Geometric mean market makers (G3Ms), such as Uniswap and Balancer, represent a widely used class of automated market makers (AMMs). These G3Ms are characterized by the following rule: the reserves of the AMM must maintain the same (weighted) geometric mean before and after each trade. This paper investigates the effects of trading fees on liquidity providers' (LP) profitability in a G3M, as well as the adverse selection faced by LPs due to arbitrage activities involving a reference market. Our work expands the model described in previous studies for G3Ms, integrating transaction fees and continuous-time arbitrage into the analysis. Within this context, we analyze G3M dynamics, characterized by stochastic storage processes, and calculate the growth rate of LP wealth. In particular, our results align with and extend the results concerning the constant product market maker, commonly referred to as Uniswap v2.

Suggested Citation

  • Cheuk Yin Lee & Shen-Ning Tung & Tai-Ho Wang, 2024. "Growth rate of liquidity provider's wealth in G3Ms," Papers 2403.18177, arXiv.org.
    • Handle: RePEc:arx:papers:2403.18177
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    References listed on IDEAS

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    1. Jason Milionis & Ciamac C. Moallemi & Tim Roughgarden, 2023. "Automated Market Making and Arbitrage Profits in the Presence of Fees," Papers 2305.14604, arXiv.org.
    2. Agostino Capponi & Ruizhe Jia, 2021. "The Adoption of Blockchain-based Decentralized Exchanges," Papers 2103.08842, arXiv.org, revised Jul 2021.
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