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Liquidity provision with $\tau$-reset strategies: a dynamic historical liquidity approach

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  • Andrey Urusov
  • Rostislav Berezovskiy
  • Anatoly Krestenko
  • Andrei Kornilov

Abstract

Since the launch of Uniswap and other AMM protocols, the DeFi industry has evolved from simple constant product functions with uniform liquidity distribution across the entire price axis to more advanced mechanisms that allow Liquidity Providers (LPs) to concentrate capital within selected price ranges. This evolution has introduced new research challenges focused on optimizing capital allocation in Decentralized Exchanges (DEXs) under dynamic market conditions. In this paper, we present a methodology for finding optimal liquidity provision strategies in DEXs within a specific family of $\tau$-reset strategies. The approach is detailed step by step and includes an original method for approximating historical liquidity within active pool ranges using a parametric model that does not rely on historical liquidity data. We find optimal LP strategies using a machine learning approach, evaluate performance over an out-of-time period, and compare the resulting strategies against a uniform benchmark. All experiments were conducted using a custom backtesting framework specifically developed for Concentrated Liquidity Market Makers (CLMMs). The effectiveness and flexibility of the proposed methodology are demonstrated across various Uniswap v3 trading pairs, and also benchmarked against an alternative backtesting and strategy development tool.

Suggested Citation

  • Andrey Urusov & Rostislav Berezovskiy & Anatoly Krestenko & Andrei Kornilov, 2025. "Liquidity provision with $\tau$-reset strategies: a dynamic historical liquidity approach," Papers 2505.15338, arXiv.org.
    • Handle: RePEc:arx:papers:2505.15338
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    References listed on IDEAS

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    1. Alexander Lipton & Vladimir Lucic & Artur Sepp, 2024. "Unified Approach for Hedging Impermanent Loss of Liquidity Provision," Papers 2407.05146, arXiv.org.
    2. Shen-Ning Tung & Tai-Ho Wang, 2024. "A mathematical framework for modelling CLMM dynamics in continuous time," Papers 2412.18580, arXiv.org.
    3. Haonan Xu & Alessio Brini, 2025. "Improving DeFi Accessibility through Efficient Liquidity Provisioning with Deep Reinforcement Learning," Papers 2501.07508, arXiv.org.
    4. Tristan Lim, 2024. "Predictive crypto-asset automated market maker architecture for decentralized finance using deep reinforcement learning," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 10(1), pages 1-29, December.
    5. Erhan Bayraktar & Asaf Cohen & April Nellis, 2024. "DEX Specs: A Mean Field Approach to DeFi Currency Exchanges," Papers 2404.09090, arXiv.org.
    6. Álvaro Cartea & Fayçal Drissi & Marcello Monga, 2023. "Predictable Losses of Liquidity Provision in Constant Function Markets and Concentrated Liquidity Markets," Applied Mathematical Finance, Taylor & Francis Journals, vol. 30(2), pages 69-93, March.
    7. Stefan Loesch & Nate Hindman & Mark B Richardson & Nicholas Welch, 2021. "Impermanent Loss in Uniswap v3," Papers 2111.09192, arXiv.org.
    8. Jason Milionis & Ciamac C. Moallemi & Tim Roughgarden, 2023. "A Myersonian Framework for Optimal Liquidity Provision in Automated Market Makers," Papers 2303.00208, arXiv.org, revised Nov 2023.
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