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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…

Trading and Market Microstructure · Quantitative Finance 2024-04-16 Erhan Bayraktar , Asaf Cohen , April Nellis

Automated Market Makers (AMMs) have cemented themselves as an integral part of the decentralized finance (DeFi) space. AMMs are a type of exchange that allows users to trade assets without the need for a centralized exchange. They form the…

Machine Learning · Computer Science 2022-11-29 Dev Churiwala , Bhaskar Krishnamachari

Concentrated Liquidity Market Makers (CLMMs) represent a fundamental innovation in market microstructure, transforming liquidity provision from passive portfolio allocation to active risk management. This evolution creates significant…

Mathematical Finance · Quantitative Finance 2026-03-31 Andrey Urusov , Rostislav Berezovskiy , Anatoly Krestenko , Andrei Kornilov , Yury Yanovich

In the ever evolving landscape of decentralized finance automated market makers (AMMs) play a key role: they provide a market place for trading assets in a decentralized manner. For so-called bluechip pairs, arbitrage activity provides a…

Statistical Finance · Quantitative Finance 2025-05-16 Abe Alexander , Lars Fritz

An automated market maker (AMM) is a state machine that manages pools of assets, allowing parties to buy and sell those assets according to a fixed mathematical formula. AMMs are typically implemented as smart contracts on blockchains, and…

Trading and Market Microstructure · Quantitative Finance 2024-01-29 Kenan Wood , Maurice Herlihy , Hammurabi Mendes , Jonad Pulaj

Automated market makers (AMMs) are one of the most prominent decentralized finance (DeFi) applications. AMMs allow users to trade different types of crypto-tokens, without the need to find a counter-party. There are several implementations…

Formal Languages and Automata Theory · Computer Science 2023-06-22 Massimo Bartoletti , James Hsin-yu Chiang , Alberto Lluch-Lafuente

In the ever evolving landscape of decentralized finance automated market makers (AMMs) play a key role: they provide a market place for trading assets in a decentralized manner. For so-called bluechip pairs, arbitrage activity provides a…

Statistical Finance · Quantitative Finance 2025-05-16 Abe Alexander , Lars Fritz

Automated Market Makers (AMMs) are used to provide liquidity for combinatorial prediction markets that would otherwise be too thinly traded. They offer both buy and sell prices for any of the doubly exponential many possible securities that…

Computer Science and Game Theory · Computer Science 2025-10-16 Maneesha Papireddygari , Xintong Wang , Bo Waggoner , David M. Pennock

Automated Market Makers (AMMs) are an integral component of the decentralized finance (DeFi) ecosystem, as they allow users to exchange crypto-assets without the need for trusted authorities or external price oracles. Although these…

Logic in Computer Science · Computer Science 2024-02-13 Daniele Pusceddu , Massimo Bartoletti

Automated Market Makers (AMMs) are a class of smart contracts on Ethereum and other blockchains that "make markets" autonomously. In other words, AMMs stand ready to trade with other market participants that interact with them, at the…

Mathematical Finance · Quantitative Finance 2022-12-22 Stefan Loesch

Automated Market Makers (AMMs) are decentralized applications that allow users to exchange crypto-tokens without the need for a matching exchange order. AMMs are one of the most successful DeFi use cases: indeed, major AMM platforms process…

Cryptography and Security · Computer Science 2022-07-20 Massimo Bartoletti , James Hsin-yu Chiang , Alberto Lluch-Lafuente

Automated Market Makers (AMMs) are emerging as a popular decentralised trading platform. In this work, we determine the optimal dynamic fees in a constant function market maker. We find approximate closed-form solutions to the control…

Trading and Market Microstructure · Quantitative Finance 2025-06-26 Leonardo Baggiani , Martin Herdegen , Leandro Sánchez-Betancourt

Automated Market Makers (AMMs) are major centers of matching liquidity supply and demand in Decentralized Finance. Their functioning relies primarily on the presence of liquidity providers (LPs) incentivized to invest their assets into a…

Machine Learning · Computer Science 2024-04-30 Viraj Nadkarni , Jiachen Hu , Ranvir Rana , Chi Jin , Sanjeev Kulkarni , Pramod Viswanath

We consider Uniswap-like automated market makers, and, specifically, constant product liquidity pools, operating on blockchains. An important feature of Uniswap is the ability for a trader to carry out a sequence of asset swaps atomically,…

Distributed, Parallel, and Cluster Computing · Computer Science 2025-01-28 Jon Michael Aanes , Jesper Balman Gravgaard , Peter Bro Miltersen , Kurt Nielsen , Mohsen Pourpouneh

Prediction markets allow traders to bet on potential future outcomes. These markets exist for weather, political, sports, and economic forecasting. Within this work we consider a decentralized framework for prediction markets using…

Mathematical Finance · Quantitative Finance 2025-01-10 Hamed Amini , Maxim Bichuch , Zachary Feinstein

Decentralized Finance (DeFi) has revolutionized financial markets by enabling complex asset-exchange protocols without trusted intermediaries. Automated Market Makers (AMMs) are a central component of DeFi, providing the core functionality…

Mathematical Finance · Quantitative Finance 2026-02-03 Marco Dessalvi , Massimo Bartoletti , Alberto Lluch-Lafuente

The always-available liquidity of automated market makers (AMMs) has been one of the most important catalysts in early cryptocurrency adoption. However, it has become increasingly evident that AMMs in their current form are not viable…

Computer Science and Game Theory · Computer Science 2023-08-10 Conor McMenamin , Vanesa Daza , Bruno Mazorra

This paper develops a rigorous mathematical framework for analyzing Concentrated Liquidity Market Makers (CLMMs) in Decentralized Finance (DeFi) within a continuous-time setting. We model the evolution of liquidity profiles as…

Mathematical Finance · Quantitative Finance 2024-12-25 Shen-Ning Tung , Tai-Ho Wang

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…

Trading and Market Microstructure · Quantitative Finance 2025-02-28 CY Yan , Steve Keol , Xo Co , Nate Leung

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…

Mathematical Finance · Quantitative Finance 2024-06-14 Álvaro Cartea , Fayçal Drissi , Marcello Monga