从暂时性损失到可持续收益：量化流动性提供者在去中心化交易所的盈利区域
From Impermanent Loss to Sustainable Gain: Quantifying Profitability Zones for Liquidity Providers on DEX
AI总结：
本文研究去中心化交易所中流动性提供者的盈利区域，通过数学模型分析套利者与AMM流动性池的互动，提出盈利区域的量化方法，为费用选择提供理论依据，增强市场稳定性。
摘要：
去中心化金融（DeFi）是区块链技术快速发展的领域，通过Web3应用提供变革性的金融服务。通过智能合约，DeFi允许开发者构建灵活且创新的金融工具。其中，去中心化交易所（DEX）交换协议（如Uniswap、Curve和Balancer）是最重要的DeFi原语之一，它们促进快速的代币交换。然而，新的交换机制也引入了新的市场不效率，这些不效率可以被套利者系统性地利用。本文专注于基于自动市场 maker（AMM）的交换协议，其中储备的乘积作为不变量。我们分析套利者与AMM流动性池的互动，并开发一个基于实证池配置的数学模型。利用此模型，我们推导了流动性提供者（LPs）和套利者联合收益的界限，提出了一种估计块数直到Impermanent Loss（IL）发生的方法，并获得池费的下限，以实现固定的目标概率在Impermanent Gain（IG）区域内保持。本文提出的框架通过量化共生盈利区域扩展了现有的LP风险评估方法，为费用选择提供了理论依据，对齐LP和套利者激励，增强市场稳定性。
英文摘要：
Decentralized Finance (DeFi) is a rapidly evolving segment of blockchain technology that enables a transformative approach to financial services through Web3 applications. By leveraging smart contracts, DeFi allows developers to build flexible and innovative financial instruments. Among the most prominent DeFi primitives by liquidity are decentralized exchange~(DEX) swap protocols~(such as Uniswap, Curve, and Balancer) that facilitate fast token-to-token exchanges. However, new exchange mechanisms also introduce new market inefficiencies that can be systematically exploited by arbitrageurs. This paper focuses on swap protocols based on the Automated Market Maker~(AMM), where the product of reserves is preserved as an invariant. We analyze the interaction between arbitrageurs and AMM liquidity pools and develop a mathematical model grounded in empirical pool configurations. Using this model, we derive bounds on the joint revenue of liquidity providers~(LPs) and arbitrageurs, propose a method to estimate the expected number of blocks until the occurrence of Impermanent Loss~(IL), and obtain a lower bound on the pool fee required to achieve a fixed target probability of staying in the Impermanent Gain (IG) zone within a block. The proposed framework extends existing LP risk-assessment methodologies by quantifying symbiotic profitability zones, providing a principled basis for fee selection that aligns LP-arbitrageur incentives and enhances market stability.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
