Optimal execution on Uniswap v2/v3 under transient price impact

Bastien Baude (), Damien Challet () and Ioane Toke ()
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Bastien Baude: MICS - Mathématiques et Informatique pour la Complexité et les Systèmes - CentraleSupélec - Université Paris-Saclay, FiQuant - Chaire de finance quantitative - MICS - Mathématiques et Informatique pour la Complexité et les Systèmes - CentraleSupélec - Université Paris-Saclay
Damien Challet: MICS - Mathématiques et Informatique pour la Complexité et les Systèmes - CentraleSupélec - Université Paris-Saclay, FiQuant - Chaire de finance quantitative - MICS - Mathématiques et Informatique pour la Complexité et les Systèmes - CentraleSupélec - Université Paris-Saclay
Ioane Toke: MICS - Mathématiques et Informatique pour la Complexité et les Systèmes - CentraleSupélec - Université Paris-Saclay, FiQuant - Chaire de finance quantitative - MICS - Mathématiques et Informatique pour la Complexité et les Systèmes - CentraleSupélec - Université Paris-Saclay

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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.

Keywords: decentralized finance; decentralized exchange; automated market makers; Uniswap; market microstructure; optimal execution; optimal scheduling problem (search for similar items in EconPapers)
Date: 2026-01-08
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