Optimal execution on Uniswap v2/v3 under transient price impact

2026-01-07

AI Summary

This study addresses the optimization of execution costs for large-position liquidations in Uniswap v2 and v3, accounting for both transient and persistent price impacts. Building upon the automated market maker (AMM) pricing mechanism, the authors develop a discrete-time model that incorporates instantaneous, decaying, and permanent price impact components, with asset price dynamics modeled via geometric Brownian motion. Using dynamic programming and numerical discretization, they derive optimal trading strategies. Key contributions include the first closed-form optimal execution strategy for Uniswap v2; a dynamic programming framework for Uniswap v3 that captures its multi-tier liquidity structure and reveals how liquidity distribution critically shapes execution paths; and a reproduction of the classic limit-order-book–style optimal execution pattern, quantitatively demonstrating the decisive role of AMM-specific liquidity configurations in shaping trading strategies.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Multiagent Systems: Mechanism Design
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Economics, Online Markets and Human Computation: Uses of LLMs and GenAI for marketplace design, bidding, and strategic interactions
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

We study the optimal liquidation of a large position on Uniswap v2 and Uniswap v3 in discrete time. The instantaneous price impact is derived from the AMM pricing rule. Transient impact is modeled to capture either exponential or approximately power-law decay, together with a permanent component. In the Uniswap v2 setting, we obtain optimal strategies in closed-form under general price dynamics. For Uniswap v3, we consider a two-layer liquidity framework, which naturally extends to multiple layers. We address the problem using dynamic programming under geometric Brownian motion dynamics and approximate the solution numerically using a discretization scheme. We obtain optimal strategies akin to classical ones in the LOB literature, with features specific to Uniswap. In particular, we show how the liquidity profile influences them.

Problem

• optimal execution
• Uniswap
• price impact
• liquidity
• AMM

Innovation

• optimal execution
• transient price impact
• Uniswap v3
• dynamic programming
• liquidity profile