Dynamics of Liquidity Distribution in Concentrated Liquidity Provision: A SPIDE Approach

Researchers use stochastic partial integro-differential equations (SPIDE) to model the dynamics of liquidity distribution in Uniswap V3 and other concentrated liquidity automated market makers. They prove the existence and uniqueness of mild solutions in a weighted L² space and reduce the SPIDE to a coupled system of linear stochastic differential equations. The model yields tractable expressions for pool reserves, pool value, and rebalancing losses. Finite-rank calibration on three Uniswap pools shows that, in two pools consistent with a stationary setting, prediction errors for active ranges are lower than a martingale benchmark.