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We suggest a framework to determine optimal trading fees for constant function market makers (CFMMs) in order to maximize liquidity provider returns. In a setting of multiple competing liquidity pools, we show that no race to the bottom…
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…
This article analytically characterizes the impermanent loss for automatic market makers in decentralized exchanges such as Uniswap or Balancer (CPMM). We present a theoretical static replication formula for the pool value using a…
Liquidity providers are essential for the function of decentralized exchanges to ensure liquidity takers can be guaranteed a counterparty for their trades. However, liquidity providers investing in liquidity pools face many risks, the most…
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…
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…
This paper studies the question whether automated market maker protocols such as Uniswap can sustainably retain a portion of their trading fees for the protocol. We approach the problem by modelling how to optimally choose a pool's take…
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…
This paper mathematically models a constant-function automated market maker (CFAMM) position as a portfolio of exotic options, known as perpetual American continuous-installment (CI) options. This model replicates an AMM position's delta at…
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…
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…
Constant-product market making functions were first introduced by Hayden Adams in 2017 to create Uniswap, a decentralised exchange on Ethereum. This enables users to exchange assets at any given rate. Some variations such as Balancer and…
Constant-function market makers (CFMMs), such as Uniswap, are automated exchanges offering trades among a set of assets. We study their technical relationship to another class of automated market makers, cost-function prediction markets. We…
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…
With the emergence of decentralized finance, new trading mechanisms called Automated Market Makers have appeared. The most popular Automated Market Makers are Constant Function Market Makers. They have been studied both theoretically and…
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…
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…
Constant Function Market Makers (CFMMs) are a family of automated market makers that enable censorship-resistant decentralized exchange on public blockchains. Arbitrage trades have been shown to align the prices reported by CFMMs with those…
This paper studies arbitrage pricing theory in financial markets with implicit transaction costs. We extend the existing theory to include the more realistic possibility that the price at which the investors trade is dependent on the traded…
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…