Paper: arXiv 2504.16542

Authors: Simon Caspar Zeller, Paul-Niklas Ken Kandora, Daniel Kirste, Niclas Kannengießer, Steffen Rebennack, Ali Sunyaev

Abstract

Concentrated liquidity automated market makers (AMMs), such as Uniswap v3, enable liquidity providers (LPs) to earn liquidity rewards by depositing tokens into liquidity pools. However, LPs often face significant financial losses driven by poorly selected liquidity provision intervals and high costs associated with frequent liquidity reallocation. To support LPs in achieving more profitable liquidity concentration, we developed a tractable stochastic optimization problem that can be used to compute optimal liquidity provision intervals for profitable liquidity provision. The developed problem accounts for the relationships between liquidity rewards, divergence loss, and reallocation costs. By formalizing optimal liquidity provision as a tractable stochastic optimization problem, we support a better understanding of the relationship between liquidity rewards, divergence loss, and reallocation costs. Moreover, the stochastic optimization problem offers a foundation for more profitable liquidity concentration.

Complexity vs Empirical Score

  • Math Complexity: 7.0/10
  • Empirical Rigor: 6.0/10 (capped from 6.5: no out-of-sample test; see penalty flags)
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper develops a tractable stochastic optimization problem, which involves advanced mathematical modeling of liquidity rewards, divergence loss, and reallocation costs. It also demonstrates utility by applying the strategy to historical on-chain trading data from Uniswap v3 and comparing it to other strategies, indicating backtest-ready empirical validation.

Research Flowchart

  flowchart TD
  A["Research Goal<br>Optimize Liquidity Provision<br>in Concentrated AMMs"] --> B{"Stochastic Optimization<br>Problem Formulation"}
  B --> C["Data Inputs<br>Price History, Fee Tiers, Gas Costs"]
  C --> D["Computational Process<br>Solve for Optimal Intervals"]
  D --> E["Key Findings<br>Optimal Intervals Reduce<br>Reallocation Costs & Divergence Loss"]
  E --> F["Outcome<br>Foundation for Profitable<br>Liquidity Concentration"]

Cited References (32)

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  2. Differential Liquidity Provision in Uniswap v3 and Implications for Contract Design✱ (2022) — link
  3. Strategic Liquidity Provision in Uniswap V3 (2023) — link
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  5. On the influence of conventional and automated market makers on market quality in cryptoeconomic systems (2024) — link
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  8. Liquidity Provision by Automated Market Makers (2020) — link
and 24 more
  1. Automated Market Making and Loss - Versus - Rebalancing (2023) — link
  2. Undergirding Bonding Curves : Supply -sovereign Automated Market Makers Enabling Liquidity and Sustainable Financing (2025) — link
  3. Complexity- Approximation Trade - Offs in Exchange Mechanisms : AMMs vs. LOBs (2024) — link
  4. Uniswap v2 Core (2020) — link
  5. Uniswap v3 Core (2021) — link
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  15. Differential Liquidity Provision in Uniswap v3 and Implications for Contract Design (2022) — link
  16. Decentralised Finance and Automated Market Making : Execution and Speculation (2022) — link
  17. G3M Impermanent Loss Dynamics (2022) — link
  18. Concentrated Liquidity Analysis in Uniswap V3 (2022) — link
  19. Stochastic dual dynamic integer programming (2019)
  20. Stochastic dual dynamic programming and its variant-a review (2023)
  21. Strategic Liquidity Provision in Uniswap V3 (2023) — link
  22. Uniswap Interface (2024) — link
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  24. Model building in mathematical programming (2013)

0 of 32 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.