Papers, ranked by score

Ordered by a blend of empirical rigor (60%) and math complexity (40%).

Dynamics of the Liquidity Profile in Concentrated Liquidity Provision: An SPIDE Approach

We model the dynamics of the liquidity profile in Uniswap~V3 and other concentrated-liquidity automated market makers with a stochastic partial integro-differential equation (SPIDE). The profile, the aggregate of all provider positions across tick space, evolves under a degenerate Sturm–Liouville o

Holy Grail Math 9 Rigor 7 ·  October 21, 2026

Dynamics of Liquidity Surfaces in Uniswap v3

This paper presents a comprehensive study on the empirical dynamics of Uniswap v3 liquidity, which we model as a time-tick surface, $L_t(x)$. Using a combination of functional principal component analysis (FPCA) and dynamic factor methods, we analyze three distinct pools over multiple sample periods

Holy Grail Math 8.5 Rigor 7 ·  September 5, 2025

Pricing and hedging for liquidity provision in Constant Function Market Making

This paper develops a robust mathematical framework for Constant Function Market Makers (CFMMs) by transitioning from traditional token reserve analyses to a coordinate system defined by price and intrinsic liquidity. We establish a canonical parametrization of the bonding curve that ensures dimensi

Holy Grail Math 8 Rigor 6 ·  March 2, 2026

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