Optimal execution on Uniswap v2/v3 under transient price impact

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Highly relevant for practitioners executing large orders on decentralized exchanges (Uniswap v2/v3). Provides actionable insights on how liquidity profiles, transient impact, and price dynamics affect optimal execution schedules. The closed-form solutions for CPAMMs and numerical framework for CLAMMs are directly applicable to DeFi trading strategies. However, the synthetic data approach and simplified liquidity assumptions limit immediate practical deployment.

The Uniswap v2 closed-form solution is relatively straightforward to implement (matrix inversion). The dynamic programming framework requires careful handling of state variables (inventory, cumulative impacts, fundamental price). The Uniswap v3 numerical scheme involves multi-dimensional grid discretization, backward recursion, linear interpolation, and transition probability computation, making it moderately complex. The paper provides pseudocode but no reference implementation.

The paper provides detailed mathematical derivations, closed-form solutions, pseudocode for the backward algorithm (Algorithm 1), and comprehensive parameter settings for all numerical experiments. Grid sizes, parameter values, and calibration procedures are explicitly stated. However, no code repository is mentioned, and the numerical scheme implementation details (e.g., interpolation methods) are partially described.