Optimal execution on Uniswap v2/v3 under transient price impact

TL;DR

This paper develops optimal trading strategies for large liquidations on Uniswap v2 and v3, accounting for transient and permanent price impacts, with solutions tailored to the unique AMM mechanisms and liquidity profiles.

Contribution

It provides the first closed-form solutions for Uniswap v2 and a dynamic programming approach for Uniswap v3, incorporating transient impact and layered liquidity structures.

Findings

Closed-form optimal strategies for Uniswap v2.

Numerical solutions for Uniswap v3 with layered liquidity.

Liquidity profile significantly influences optimal trading strategies.

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.