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Related papers: Axioms for Constant Function Market Makers

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Automated market makers (AMMs) are automata that trade electronic assets at rates set by mathematical formulas. AMMs are usually implemented by smart contracts on blockchains. In practice, AMMs are often composed: and outputs from AMMs can…

Distributed, Parallel, and Cluster Computing · Computer Science 2021-09-01 Daniel Engel , Maurice Herlihy

The rise of Ethereum and other blockchains that support smart contracts has led to the creation of decentralized exchanges (DEXs), such as Uniswap, Balancer, Curve, mStable, and SushiSwap, which enable agents to trade cryptocurrencies…

Optimization and Control · Mathematics 2021-07-28 Guillermo Angeris , Akshay Agrawal , Alex Evans , Tarun Chitra , Stephen Boyd

Constant Product Market Makers use fees that are typically fixed proportions of trade size. When these fees are automatically reinvested into the pool, as in Uniswap~V2 and some designs of Uniswap V4, the final state after a trade can…

Distributed, Parallel, and Cluster Computing · Computer Science 2026-05-01 Andrey Voronin , Roman Vlasov , Vladimir Gorgadze , Andrey Seoev , Yury Yanovich

This paper demonstrates that Automated Market Maker (AMM) based markets, such as those using constant product formulas (e.g., Uniswap), are inherently path-dependent. We prove mathematically that the sequence of operations in AMMs…

Computational Engineering, Finance, and Science · Computer Science 2025-03-04 Keroshan Pillay

This work analytically characterizes impermanent loss for automated market makers (AMMs) in decentralized markets such as Uniswap or Balancer (CPMM). We derive a static replication formula for the pool's value using a combination of…

Risk Management · Quantitative Finance 2025-03-31 Agustin Muñoz Gonzalez , Juan Ignacio Sequeira , Ariel Dembling

Automated Market Makers (AMMs), as a core infrastructure of decentralized finance (DeFi), uniquely drive on-chain asset pricing through a deterministic reserve ratio mechanism. Unlike traditional markets, AMM price dynamics is triggered…

Machine Learning · Computer Science 2026-04-23 Huaiyu Jia , Jiehshun You , Yizhi Luo , Jingyu Liu , Shuo Sun

We consider the social welfare that can be facilitated by a constant function market maker (CFMM). When there is sufficient liquidity available to the CFMM, it can approximate the optimal social welfare when all users transactions are…

Computer Science and Game Theory · Computer Science 2022-11-24 Bruno Mazorra , Nicolás Della Penna

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

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

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

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

We design a prediction market to recover a complete and fully general probability distribution over a random variable. Traders buy and sell interval securities that pay \$1 if the outcome falls into an interval and \$0 otherwise. Our market…

Computer Science and Game Theory · Computer Science 2021-02-17 Miroslav Dudík , Xintong Wang , David M. Pennock , David M. Rothschild

Market making (MM) through Reinforcement Learning (RL) has attracted significant attention in financial trading. With the development of Large Language Models (LLMs), more and more attempts are being made to apply LLMs to financial areas. A…

Artificial Intelligence · Computer Science 2026-01-30 Tianhao Fu , Xinxin Xu , Weichen Xu , Jue Chen , Ruilong Ren , Bowen Deng , Xinyu Zhao , Jian Cao , Xixin Cao

Constant function market makers (CFMMs) such as Uniswap have facilitated trillions of dollars of digital asset trades and have billions of dollars of liquidity. One natural question is how to optimally route trades across a network of CFMMs…

Optimization and Control · Mathematics 2023-02-13 Theo Diamandis , Max Resnick , Tarun Chitra , Guillermo Angeris

We propose the Artificial Continuous Prediction Market (ACPM) as a means to predict a continuous real value, by integrating a range of data sources and aggregating the results of different machine learning (ML) algorithms. ACPM adapts the…

Artificial Intelligence · Computer Science 2015-08-12 Fatemeh Jahedpari , Marina De Vos , Sattar Hashemi , Benjamin Hirsch , Julian Padget

The role of a market maker is to simultaneously offer to buy and sell quantities of goods, often a financial asset such as a share, at specified prices. An automated market maker (AMM) is a mechanism that offers to trade according to some…

Computer Science and Game Theory · Computer Science 2024-02-15 Michael J. Curry , Zhou Fan , David C. Parkes

We consider the market microstructure of automated market makers (AMMs) from the perspective of liquidity providers (LPs). Our central contribution is a ``Black-Scholes formula for AMMs''. We identify the main adverse selection cost…

Mathematical Finance · Quantitative Finance 2024-05-29 Jason Milionis , Ciamac C. Moallemi , Tim Roughgarden , Anthony Lee Zhang

In decentralized finance (DeFi), designing fixed-income lending automated market makers (AMMs) is extremely challenging due to time-related complexities. Moreover, existing protocols only support single-maturity lending. Building upon the…

Cryptography and Security · Computer Science 2025-12-19 Tianyi Ma

Designing automated market makers (AMMs) is crucial for decentralized token exchanges in cryptoeconomic systems. At the intersection of software engineering and economics, AMM design is complex and, if done incorrectly, can lead to…

Trading and Market Microstructure · Quantitative Finance 2025-03-24 Daniel Kirste , Niclas Kannengießer , Ricky Lamberty , Ali Sunyaev

In this paper we analyze constant product market makers (CPMMs). We formalize the liquidity providers' profitability conditions and introduce a concept we call the profitability frontier in the xyk-space. We study the effect of mint and…

General Finance · Quantitative Finance 2023-03-29 Tobias Bitterli , Fabian Schär