Automated Market Makers: A Stochastic Optimization Approach for Profitable Liquidity Concentration

ArXiv ID: 2504.16542 “View on arXiv”

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.

Keywords: Concentrated Liquidity, Automated Market Maker (AMM), Stochastic Optimization, Divergence Loss, Liquidity Provision, Crypto/DeFi

Complexity vs Empirical Score

  • Math Complexity: 7.0/10
  • Empirical Rigor: 6.5/10
  • Quadrant: Holy Grail
  • Why: 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.
  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"]