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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…

Trading and Market Microstructure · Quantitative Finance 2024-07-25 Marcello Monga

Automated Market Makers (AMMs) are a central component of decentralized exchanges, yet their equilibrium foundations and microeconomic mechanisms remain incompletely understood. This paper develops a dynamic equilibrium framework for…

General Economics · Economics 2026-03-10 Chengqi Zang , Zhenghui Wang , Weitong Zhang

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…

Trading and Market Microstructure · Quantitative Finance 2025-04-24 Simon Caspar Zeller , Paul-Niklas Ken Kandora , Daniel Kirste , Niclas Kannengießer , Steffen Rebennack , Ali Sunyaev

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

The emergence of Concentrated Liquidity Market Makers (CLMMs) has made liquidity provision on decentralized exchanges an active and risk-sensitive task. However, the standalone profitability of liquidity provision remains unclear for…

Trading and Market Microstructure · Quantitative Finance 2026-04-27 Andrey Urusov , Rostislav Berezovskiy , Anatoly Krestenko , Andrei Kornilov

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

In decentralized finance, any individual can pool their assets into an automated market maker (AMM) -- herein we focus on the constant product market maker (CPMM) -- in exchange for a claim on a fraction of future pool assets and fees…

Mathematical Finance · Quantitative Finance 2026-01-27 Maxim Bichuch , Zachary Feinstein

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…

Trading and Market Microstructure · Quantitative Finance 2025-01-15 Thanos Drossos , Daniel Kirste , Niclas Kannengießer , Ali Sunyaev

Decentralized finance (DeFi) has revolutionized the financial landscape, with protocols like Uniswap offering innovative automated market-making mechanisms. This article explores the development of a backtesting framework specifically…

Mathematical Finance · Quantitative Finance 2024-10-15 Andrey Urusov , Rostislav Berezovskiy , Yury Yanovich

Liquidity providers (LPs) are essential figures in the operation of automated market makers (AMMs); in exchange for transaction fees, LPs lend the liquidity that allows AMMs to operate. While many prior works have studied the incentive…

Computer Science and Game Theory · Computer Science 2025-09-22 Bruno Llacer Trotti , Weizhao Tang , Rachid El-Azouzi , Giulia Fanti , Daniel Sadoc Menasche

Decentralised automated market makers (AMMs) have gained significant attention recently. We propose an adaptive and automated Dynamic Function Market Maker (DFMM) that addresses challenges in this space. Our DFMM protocol includes a data…

General Finance · Quantitative Finance 2023-07-26 Arman Abgaryan , Utkarsh Sharma

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…

Mathematical Finance · Quantitative Finance 2026-03-03 Jimmy Risk , 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

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

The study proposes a quote-driven predictive automated market maker (AMM) platform with on-chain custody and settlement functions, alongside off-chain predictive reinforcement learning capabilities to improve liquidity provision of…

Trading and Market Microstructure · Quantitative Finance 2023-01-27 Tristan Lim

This article analytically characterizes the impermanent loss of concentrated liquidity provision for automatic market makers in decentralised markets such as Uniswap. We propose two static replication formulas for the impermanent loss by a…

General Finance · Quantitative Finance 2023-03-03 Jun Deng , Hua Zong , Yun Wang

Automated market makers (AMMs) are a new prototype of decentralised exchanges which are revolutionising market interactions. The majority of AMMs are constant product markets (CPMs) where exchange rates are set by a trading function. This…

Trading and Market Microstructure · Quantitative Finance 2025-06-19 Álvaro Cartea , Fayçal Drissi , Marcello Monga

Concentrated liquidity (CL) provisioning is a way how to improve the capital efficiency of Automated Market Makers (AMM). Allowing liquidity providers to use leverage is a step towards even higher capital efficiency. A number of…

Trading and Market Microstructure · Quantitative Finance 2024-09-20 Atis Elsts , Krešimir Klas

We examine how the introduction of concentrated liquidity has changed the liquidity provision market in automated market makers such as Uniswap. To this end, we compare average liquidity provider returns from trading fees before and after…

Trading and Market Microstructure · Quantitative Finance 2023-10-30 Robin Fritsch

Decentralized Exchanges (DEXs) are new types of marketplaces leveraging Blockchain technology. They allow users to trade assets with Automatic Market Makers (AMM), using funds provided by liquidity providers, removing the need for order…

Computer Science and Game Theory · Computer Science 2023-02-08 Yogev Bar-On , Yishay Mansour
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