Liquidity Provision

Equilibrium Liquidity and Risk Offsetting in Decentralised Markets ArXiv ID: 2512.19838 “View on arXiv” Authors: Fayçal Drissi, Xuchen Wu, Sebastian Jaimungal Abstract We develop an economic model of decentralised exchanges (DEXs) in which risk-averse liquidity providers (LPs) manage risk in a centralised exchange (CEX) based on preferences, information, and trading costs. Rational, risk-averse LPs anticipate the frictions associated with replication and manage risk primarily by reducing the reserves supplied to the DEX. Greater aversion reduces the equilibrium viability of liquidity provision, resulting in thinner markets and lower trading volumes. Greater uninformed demand supports deeper liquidity, whereas higher fundamental price volatility erodes it. Finally, while moderate anticipated price changes can improve LP performance, larger changes require more intensive trading in the CEX, generate higher replication costs, and induce LPs to reduce liquidity supply. ...

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. ...

Optimal Fees for Liquidity Provision in Automated Market Makers ArXiv ID: 2508.08152 “View on arXiv” Authors: Steven Campbell, Philippe Bergault, Jason Milionis, Marcel Nutz Abstract Passive liquidity providers (LPs) in automated market makers (AMMs) face losses due to adverse selection (LVR), which static trading fees often fail to offset in practice. We study the key determinants of LP profitability in a dynamic reduced-form model where an AMM operates in parallel with a centralized exchange (CEX), traders route their orders optimally to the venue offering the better price, and arbitrageurs exploit price discrepancies. Using large-scale simulations and real market data, we analyze how LP profits vary with market conditions such as volatility and trading volume, and characterize the optimal AMM fee as a function of these conditions. We highlight the mechanisms driving these relationships through extensive comparative statics, and confirm the model’s relevance through market data calibration. A key trade-off emerges: fees must be low enough to attract volume, yet high enough to earn sufficient revenues and mitigate arbitrage losses. We find that under normal market conditions, the optimal AMM fee is competitive with the trading cost on the CEX and remarkably stable, whereas in periods of very high volatility, a high fee protects passive LPs from severe losses. These findings suggest that a threshold-type dynamic fee schedule is both robust enough to market conditions and improves LP outcomes. ...

On the hidden costs of passive investing ArXiv ID: 2506.21775 “View on arXiv” Authors: Iro Tasitsiomi Abstract Passive investing has gained immense popularity due to its low fees and the perceived simplicity of focusing on zero tracking error, rather than security selection. However, our analysis shows that the passive (zero tracking error) approach of waiting until the market close on the day of index reconstitution to purchase a stock (that was announced days earlier as an upcoming addition) results in costs amounting to hundreds of basis points compared to strategies that involve gradually acquiring a small portion of the required shares in advance with minimal additional tracking errors. In addition, we show that under all scenarios analyzed, a trader who builds a small inventory post-announcement and provides liquidity at the reconstitution event can consistently earn several hundreds of basis points in profit and often much more, assuming minimal risk. ...

Automated Market Makers: A Stochastic Optimization Approach for Profitable Liquidity Concentration ArXiv ID: 2504.16542 “View on arXiv” Authors: Simon Caspar Zeller, Paul-Niklas Ken Kandora, Daniel Kirste, Niclas Kannengießer, Steffen Rebennack, Ali Sunyaev Abstract Concentrated liquidity automated market makers (AMMs), such as Uniswap v3, enable liquidity providers (LPs) to earn liquidity rewards by depositing tokens into liquidity pools. However, LPs often face significant financial losses driven by poorly selected liquidity provision intervals and high costs associated with frequent liquidity reallocation. To support LPs in achieving more profitable liquidity concentration, we developed a tractable stochastic optimization problem that can be used to compute optimal liquidity provision intervals for profitable liquidity provision. The developed problem accounts for the relationships between liquidity rewards, divergence loss, and reallocation costs. By formalizing optimal liquidity provision as a tractable stochastic optimization problem, we support a better understanding of the relationship between liquidity rewards, divergence loss, and reallocation costs. Moreover, the stochastic optimization problem offers a foundation for more profitable liquidity concentration. ...

A Simple Strategy to Deal with Toxic Flow ArXiv ID: 2503.18005 “View on arXiv” Authors: Unknown Abstract We model the trading activity between a broker and her clients (informed and uninformed traders) as an infinite-horizon stochastic control problem. We derive the broker’s optimal dealing strategy in closed form and use this to introduce an algorithm that bypasses the need to calibrate individual parameters, so the dealing strategy can be executed in real-world trading environments. Finally, we characterise the discount in the price of liquidity a broker offers clients. The discount strikes the optimal balance between maximising the order flow from the broker’s clients and minimising adverse selection losses to the informed traders. ...

Better market Maker Algorithm to Save Impermanent Loss with High Liquidity Retention ArXiv ID: 2502.20001 “View on arXiv” Authors: Unknown Abstract Decentralized exchanges (DEXs) face persistent challenges in liquidity retention and user engagement due to inefficiencies in conventional automated market maker (AMM) designs. This work proposes a dual-mechanism framework to address these limitations: a ``Better Market Maker (BMM)’’, which is a liquidity-optimized AMM based on a power-law invariant ($X^nY = K$, $n = 4$), and a dynamic rebate system (DRS) for redistributing transaction fees. The segment-specific BMM reduces impermanent loss by 36% compared to traditional constant-product ($XY = K$) models, while retaining 3.98x more liquidity during price volatility. The DRS allocates fees ($γV$, $γ\in {“0.003, 0.005, 0.01"}$) with a rebate ratio $ρ\in [“0.3, 0.4”]$ to incentivize trader participation and maintain continuous capital injection. Simulations under high-volatility conditions demonstrate impermanent loss reductions of 36.0% and 40% higher user engagement compared to static fee models. By segmenting markets into high-, mid-, and low-volatility regimes, the framework achieves liquidity depth comparable to centralized exchanges (CEXs) while maintaining decentralized governance and retaining value within the cryptocurrency ecosystem. ...

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. ...

Market Making with Fads, Informed, and Uninformed Traders ArXiv ID: 2501.03658 “View on arXiv” Authors: Unknown Abstract We characterise the solutions to a continuous-time optimal liquidity provision problem in a market populated by informed and uninformed traders. In our model, the asset price exhibits fads – these are short-term deviations from the fundamental value of the asset. Conditional on the value of the fad, we model how informed traders and uninformed traders arrive in the market. The market maker knows of the two groups of traders but only observes the anonymous order arrivals. We study both, the complete information and the partial information versions of the control problem faced by the market maker. In such frameworks, we characterise the value of information, and we find the price of liquidity as a function of the proportion of informed traders in the market. Lastly, for the partial information setup, we explore how to go beyond the Kalman-Bucy filter to extract information about the fad from the market arrivals. ...

Automated Market Making: the case of Pegged Assets ArXiv ID: 2411.08145 “View on arXiv” Authors: Unknown Abstract In this paper, we introduce a novel framework to model the exchange rate dynamics between two intrinsically linked cryptoassets, such as stablecoins pegged to the same fiat currency or a liquid staking token and its associated native token. Our approach employs multi-level nested Ornstein-Uhlenbeck (OU) processes, for which we derive key properties and develop calibration and filtering techniques. Then, we design an automated market maker (AMM) model specifically tailored for the swapping of closely related cryptoassets. Distinct from existing models, our AMM leverages the unique exchange rate dynamics provided by the multi-level nested OU processes, enabling more precise risk management and enhanced liquidity provision. We validate the model through numerical simulations using real-world data for the USDC/USDT and wstETH/WETH pairs, demonstrating that it consistently yields efficient quotes. This approach offers significant potential to improve liquidity in markets for pegged assets. ...