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Automated Market Makers (AMMs) are essential in Decentralized Finance (DeFi) as they match liquidity supply with demand. They function through liquidity providers (LPs) who deposit assets into liquidity pools. However, the asset trading…

Systems and Control · Electrical Eng. & Systems 2025-04-01 Viraj Nadkarni , Sanjeev Kulkarni , Pramod Viswanath

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…

Trading and Market Microstructure · Quantitative Finance 2025-02-05 Masaaki Fukasawa , Basile Maire , Marcus Wunsch

As an integral part of the decentralized finance (DeFi) ecosystem, decentralized exchanges (DEXs) with automated market maker (AMM) protocols have gained massive traction with the recently revived interest in blockchain and distributed…

Trading and Market Microstructure · Quantitative Finance 2023-03-16 Jiahua Xu , Krzysztof Paruch , Simon Cousaert , Yebo Feng

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

The asset trading volume on blockchain-based exchanges (DEX) increased substantially since the advent of Automated Market Makers (AMM). Yet, AMMs and their forks compete on the same blockchain, incurring unnecessary network and block-space…

Cryptography and Security · Computer Science 2021-06-21 Liyi Zhou , Kaihua Qin , Arthur Gervais

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

Within this work we consider an axiomatic framework for Automated Market Makers (AMMs). AMMs are smart contracts that set prices for swaps on a pool of assets. By imposing reasonable axioms on the underlying utility function, we are able to…

Mathematical Finance · Quantitative Finance 2025-02-04 Maxim Bichuch , Zachary Feinstein

This paper studies liquid staking tokens (LSTs) on automated market makers (AMMs), both theoretically and empirically. LSTs are tokenized representations of staked assets on proof-of-stake blockchains. First, we model LST-liquidity on AMMs…

Cryptography and Security · Computer Science 2024-07-22 Krzysztof Gogol , Robin Fritsch , Malte Schlosser , Johnnatan Messias , Benjamin Kraner , Claudio Tessone

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) allocate fee revenue \textit{proportional} to the amount of liquidity investors deposit. In this paper, we study the economic consequences of the competition between passive liquidity providers (LPs) caused by…

Computer Science and Game Theory · Computer Science 2024-08-06 Julian Ma , Davide Crapis

In this paper, we analyze traders' behavior within both centralized exchanges (CEXs) and decentralized exchanges (DEXs), focusing on the volatility of Bitcoin prices and the trading activity of investors engaged in perpetual future…

Trading and Market Microstructure · Quantitative Finance 2024-04-26 Erdong Chen , Mengzhong Ma , Zixin Nie

The limit order book mechanism has been the core trading mechanism of the modern financial market. In the cryptocurrency market, centralized exchanges also adopt this limit order book mechanism and a centralized matching engine dynamically…

Computational Engineering, Finance, and Science · Computer Science 2022-12-21 Yeonwoo Jeong , Chanyoung Jeoung , Hosan Jeong , SangYoon Han , Juntae Kim

Automated market makers (AMMs) quote prices from pool state rather than from a limit order book. AMM pools often stay close to a reference price because arbitrageurs correct profitable mispricing. A large part of decentralized finance…

Computational Engineering, Finance, and Science · Computer Science 2026-05-08 Peihao Li , Nadia Dahmani , Wenqi Cai

Automated Market Makers (AMMs) hold assets and are constantly being rebalanced by external arbitrageurs to match external market prices. Loss-versus-rebalancing (LVR) is a pivotal metric for measuring how an AMM pool performs for its…

Trading and Market Microstructure · Quantitative Finance 2024-11-01 Matthew Willetts , Christian Harrington

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.…

Trading and Market Microstructure · Quantitative Finance 2024-11-14 Philippe Bergault , Louis Bertucci , David Bouba , Olivier Guéant , Julien Guilbert

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

We consider the impact of trading fees on the profits of arbitrageurs trading against an automated market maker (AMM) or, equivalently, on the adverse selection incurred by liquidity providers (LPs) due to arbitrage. We extend the model of…

Mathematical Finance · Quantitative Finance 2025-07-24 Jason Milionis , Ciamac C. Moallemi , Tim Roughgarden

Decentralized exchanges (DEXes) have introduced an innovative trading mechanism, where it is not necessary to match buy-orders and sell-orders to execute a trade. DEXes execute each trade individually, and the exchange rate is automatically…

Computational Finance · Quantitative Finance 2021-10-12 Lioba Heimbach , Ye Wang , Roger Wattenhofer

This paper introduces and analyzes \emph{defensive rebalancing}, a novel mechanism for protecting constant-function market makers (CFMMs) from value leakage due to arbitrage. A \emph{rebalancing} transfers assets directly from one CFMM's…

Computer Science and Game Theory · Computer Science 2026-01-29 Sam Devorsetz , Maurice Herlihy

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