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Related papers: Concentrated Liquidity with Leverage

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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

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

In Decentralized Finance (DeFi), automated market makers typically implement liquidity provisioning protocols. These protocols allow third-party liquidity providers (LPs) to provide assets to facilitate trade in exchange for fees. This…

Computer Science and Game Theory · Computer Science 2025-07-29 Adithya Bhaskara , Rafael Frongillo , Maneesha Papireddygari

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

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

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

The trustless nature of permissionless blockchains renders overcollateralization a key safety component relied upon by decentralized finance (DeFi) protocols. Nonetheless, factors such as price volatility may undermine this mechanism. In…

General Finance · Quantitative Finance 2021-12-14 Daniel Perez , Sam M. Werner , Jiahua Xu , Benjamin Livshits

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

We develop a mathematical framework to optimize leveraged staking ("loopy") strategies in Decentralized Finance (DeFi), in which a staked asset is supplied as collateral, the underlying is borrowed and re-staked, and the loop can be…

Mathematical Finance · Quantitative Finance 2026-01-21 Bastien Baude , Vincent Danos , Hamza El Khalloufi

Automated market makers with concentrated liquidity capabilities are programmable at the tick level. The maximization of earned fees, plus depreciated reserves, is a convex optimization problem whose vector solution gives the best provision…

Portfolio Management · Quantitative Finance 2024-05-30 Corinne Powers

In decentralized finance ("DeFi"), automated market makers (AMMs) enable traders to programmatically exchange one asset for another. Such trades are enabled by the assets deposited by liquidity providers (LPs). The goal of this paper is to…

Computer Science and Game Theory · Computer Science 2023-11-29 Jason Milionis , Ciamac C. Moallemi , Tim Roughgarden

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

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

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 reshaped the possibilities of reserve banking in the form of the Collateralized Debt Position (CDP). Key to the safety of CDPs is the money supply architecture that enables issued debt to maintain its value.…

Risk Management · Quantitative Finance 2024-07-19 Yuval Boneh

Automated market makers are a popular mechanism used on decentralized exchange, through which users trade assets with each other directly and automatically through a liquidity pool and a fixed pricing function. The liquidity provider…

Mathematical Finance · Quantitative Finance 2024-11-27 Xue Dong He , Chen Yang , Yutian Zhou

Lending protocols are one of the main applications of Decentralized Finance (DeFi), enabling crypto-assets loan markets with a total value estimated in the tens of billions of dollars. Unlike traditional lending systems, these protocols…

Computer Science and Game Theory · Computer Science 2025-06-19 Massimo Bartoletti , Enrico Lipparini

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

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
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