Uniswap V3

Adaptive Dueling Double Deep Q-networks in Uniswap V3 Replication and Extension with Mamba ArXiv ID: 2511.22101 “View on arXiv” Authors: Zhaofeng Zhang Abstract The report goes through the main steps of replicating and improving the article “Adaptive Liquidity Provision in Uniswap V3 with Deep Reinforcement Learning.” The replication part includes how to obtain data from the Uniswap Subgraph, details of the implementation, and comments on the results. After the replication, I propose a new structure based on the original model, which combines Mamba with DDQN and a new reward function. In this new structure, I clean the data again and introduce two new baselines for comparison. As a result, although the model has not yet been applied to all datasets, it shows stronger theoretical support than the original model and performs better in some tests. ...

Dynamics of Liquidity Surfaces in Uniswap v3 ArXiv ID: 2509.05013 “View on arXiv” Authors: Jimmy Risk, Shen-Ning Tung, Tai-Ho Wang Abstract 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. Our findings offer three main contributions: a statistical characterization of automated market maker liquidity, an interpretable and portable basis for dimension reduction, and a robust analysis of liquidity dynamics using rolling window metrics. For the 5 bps pools, the leading empirical eigenfunctions explain the majority of cross-tick variation and remain stable, aligning closely with a low-order Legendre polynomial basis. This alignment provides a parsimonious and interpretable structure, similar to the dynamic Nelson-Siegel method for yield curves. The factor coefficients exhibit a time series structure well-captured by AR(1) models with clear GARCH-type heteroskedasticity and heavy-tailed innovations. ...

Liquidity provision of utility indifference type in decentralized exchanges ArXiv ID: 2502.01931 “View on arXiv” Authors: Unknown Abstract We present a mathematical formulation of liquidity provision in decentralized exchanges. We focus on constant function market makers of utility indifference type, which include constant product market makers with concentrated liquidity as a special case. First, we examine no-arbitrage conditions for a liquidity pool and compute an optimal arbitrage strategy when there is an external liquid market. Second, we show that liquidity provision suffers from impermanent loss unless a transaction fee is levied under the general framework with concentrated liquidity. Third, we establish the well-definedness of arbitrage-free reserve processes of a liquidity pool in continuous-time and show that there is no loss-versus-rebalancing under a nonzero fee if the external market price is continuous. We then argue that liquidity provision by multiple liquidity providers can be understood as liquidity provision by a representative liquidity provider, meaning that the analysis boils down to that for a single liquidity provider. Last, but not least, we give an answer to the fundamental question in which sense the very construction of constant function market makers with concentrated liquidity in the popular platform Uniswap v3 is optimal. ...

Automated Market Makers: Toward More Profitable Liquidity Provisioning Strategies ArXiv ID: 2501.07828 “View on arXiv” Authors: Unknown Abstract To trade tokens in cryptoeconomic systems, automated market makers (AMMs) typically rely on liquidity providers (LPs) that deposit tokens in exchange for rewards. To profit from such rewards, LPs must use effective liquidity provisioning strategies. However, LPs lack guidance for developing such strategies, which often leads them to financial losses. We developed a measurement model based on impermanent loss to analyze the influences of key parameters (i.e., liquidity pool type, position duration, position range size, and position size) of liquidity provisioning strategies on LPs’ returns. To reveal the influences of those key parameters on LPs’ profits, we used the measurement model to analyze 700 days of historical liquidity provision data of Uniswap v3. By uncovering the influences of key parameters of liquidity provisioning strategies on profitability, this work supports LPs in developing more profitable strategies. ...

Automated Market Making and Decentralized Finance ArXiv ID: 2407.16885 “View on arXiv” Authors: Unknown Abstract Automated market makers (AMMs) are a new type of trading venues which are revolutionising the way market participants interact. At present, the majority of AMMs are constant function market makers (CFMMs) where a deterministic trading function determines how markets are cleared. Within CFMMs, we focus on constant product market makers (CPMMs) which implements the concentrated liquidity (CL) feature. In this thesis we formalise and study the trading mechanism of CPMMs with CL, and we develop liquidity provision and liquidity taking strategies. Our models are motivated and tested with market data. We derive optimal strategies for liquidity takers (LTs) who trade orders of large size and execute statistical arbitrages. First, we consider an LT who trades in a CPMM with CL and uses the dynamics of prices in competing venues as market signals. We use Uniswap v3 data to study price, liquidity, and trading cost dynamics, and to motivate the model. Next, we consider an LT who trades a basket of crypto-currencies whose constituents co-move. We use market data to study lead-lag effects, spillover effects, and causality between trading venues. We derive optimal strategies for strategic liquidity providers (LPs) who provide liquidity in CPMM with CL. First, we use stochastic control tools to derive a self-financing and closed-form optimal liquidity provision strategy where the width of the LP’s liquidity range is determined by the profitability of the pool, the dynamics of the LP’s position, and concentration risk. Next, we use a model-free approach to solve the problem of an LP who provides liquidity in multiple CPMMs with CL. We do not specify a model for the stochastic processes observed by LPs, and use a long short-term memory (LSTM) neural network to approximate the optimal liquidity provision strategy. ...

DEX Specs: A Mean Field Approach to DeFi Currency Exchanges ArXiv ID: 2404.09090 “View on arXiv” Authors: Unknown Abstract We investigate the behavior of liquidity providers (LPs) by modeling a decentralized cryptocurrency exchange (DEX) based on Uniswap v3. LPs with heterogeneous characteristics choose optimal liquidity positions subject to uncertainty regarding the size of exogenous incoming transactions and the prices of assets in the wider market. They engage in a game among themselves, and the resulting liquidity distribution determines the exchange rate dynamics and potential arbitrage opportunities of the pool. We calibrate the distribution of LP characteristics based on Uniswap data and the equilibrium strategy resulting from this mean-field game produces pool exchange rate dynamics and liquidity evolution consistent with observed pool behavior. We subsequently introduce Maximal Extractable Value (MEV) bots who perform Just-In-Time (JIT) liquidity attacks, and develop a Stackelberg game between LPs and bots. This addition results in more accurate simulated pool exchange rate dynamics and stronger predictive power regarding the evolution of the pool liquidity distribution. ...

Decentralised Finance and Automated Market Making: Predictable Loss and Optimal Liquidity Provision ArXiv ID: 2309.08431 “View on arXiv” Authors: Unknown Abstract Constant product markets with concentrated liquidity (CL) are the most popular type of automated market makers. In this paper, we characterise the continuous-time wealth dynamics of strategic LPs who dynamically adjust their range of liquidity provision in CL pools. Their wealth results from fee income, the value of their holdings in the pool, and rebalancing costs. Next, we derive a self-financing and closed-form optimal liquidity provision strategy where the width of the LP’s liquidity range is determined by the profitability of the pool (provision fees minus gas fees), the predictable losses (PL) of the LP’s position, and concentration risk. Concentration risk refers to the decrease in fee revenue if the marginal exchange rate (akin to the midprice in a limit order book) in the pool exits the LP’s range of liquidity. When the drift in the marginal rate is stochastic, we show how to optimally skew the range of liquidity to increase fee revenue and profit from the expected changes in the marginal rate. Finally, we use Uniswap v3 data to show that, on average, LPs have traded at a significant loss, and to show that the out-of-sample performance of our strategy is superior to the historical performance of LPs in the pool we consider. ...