Method constructs CFMMs matching desired payoffs.
problem Creating CFMMs with specific payoff functions.
method Uses convex analysis and Fenchel conjugacy.
result Every concave, nonnegative, nondecreasing, 1-homogeneous payoff has a corresponding convex CFMM.
An efficient algorithm optimizes trades across CFMM networks.
problem Optimizing trades through a network of CFMMs for maximum utility.
method Decomposition method to solve the routing problem.
result Significant performance improvements over commercial solvers.
Geometric framework for CFMMs simplifies many results.
problem Understanding the behavior of CFMMs without strong conditions.
method Developed a geometric framework encompassing known results.
result CFMMs have a canonical trading function with specific properties.
Optimal fees for G3Ms align LP value with market accuracy.
problem Optimal fees for G3Ms to attract liquidity without sacrificing accuracy.
method Developed a framework for determining LP value with fees for G3Ms under diffusion.
result LPs prefer G3Ms over other strategies as fees approach zero.
New market makers improve on existing models in DeFi.
problem Improving liquidity and efficiency in decentralized finance.
method Developed a new family of market makers based on generalized means.
result G3Ms offer properties preferable to existing models.
This paper analyzes a time-dependent CFMM called RMM-01, focusing on its pricing and stability.
problem Analyzing the pricing and stability of a time-dependent CFMM called RMM-01.
method Introducing the general framework for CFMMs, analyzing pricing properties, and examining time-varying price stability.
result Determining parameter bounds for RMM-01 to achieve a more stable price than Uniswap.
Study on CFMMs pricing and hedging, developing models for LP and derivatives valuation.
problem Valuation and hedging of liquidity provider mechanisms in CFMMs.
method Developed a model with two types of traders, simulated their behavior, and calculated PnL.
result Foundations for estimating CFMM derivatives and understanding fair price distribution.
Optimal crypto asset routing with CFMMs, including fixed costs.
problem Optimizing order execution on a network of CFMMs with fixed costs.
method Convex optimization for no fixed costs, mixed-integer convex for fixed costs, heuristics for approximate solutions.
result Approximate solutions to optimal routing and arbitrage certification problems.
The paper defines price sensitivity and liquidity in CFMMs and links it to curvature.
problem Understanding the relationship between CFMM curvature and market performance.
method Proposes a definition of price sensitivity and liquidity, and links it to CFMM curvature.
result Curvature of CFMMs affects market performance and liquidity provider incentives.
Optimal fees for CFMMs prevent liquidity pools from competing to the bottom.
problem Maximizing liquidity provider returns in CFMMs with multiple pools.
method Theoretical and numerical analysis of Nash equilibria for optimal fees.
result Pure Nash equilibria of optimal fees exist for CFMMs using Uniswap's trade function.
Paper shows how to replicate payoffs without oracles in CFMMs.
problem Replicating payoffs without oracles in CFMMs.
method Using liquidity provider shares in CFMMs to match any monotonic payoff.
result Explicit method and formula for trading functions and earnings.
The paper analyzes CFMMs to ensure accurate price reporting.
problem Ensuring accurate price reporting for CFMMs.
method Analyzes CFMMs under general assumptions to incentivize correct price reporting.
result Agents are incentivized to correctly report asset prices in a computationally efficient way.
This paper analyzes microstructure dynamics in coupled markets using CFMMs.
problem Quantifying contributions of CFMMs to market dynamics in coupled markets.
method Examined constant function market makers (CFMMs) in coupled markets, focusing on basket inflation/deflation.
result CFMMs contribute significantly to basket inflation/deflation in coupled markets.
CFMMs solve complex multi-asset trades via convex optimization.
problem Complex multi-asset trades in decentralized exchanges.
method Formulate multi-asset trades as convex optimization problems.
result Efficiently solve multi-asset trades using convex optimization.
Optimizes trading in CFMMs and exchanges using deep learning.
problem Optimizing trading strategies in CFMMs and exchanges.
method Develops a model accounting for interaction between CFMMs and exchanges, employs deep Galerkin method to solve dynamic programming equation.
result Optimal strategy outperforms naïve strategies and is not prone to price slippage.
A new method for creating derivatives without oracles.
problem Lack of trust in external oracles for derivatives pricing.
method Using Replicating Market Makers (RMMs) to create derivative instruments.
result Demonstrated the feasibility of on-chain expiring options without oracles.
Maximal extractable value in CFMMs can degrade or improve routing quality, with reordering MEV showing logarithmic impact.
problem Maximal extractable value in constant function market makers (CFMMs) and its impact on routing quality.
method Game theoretic analysis of MEV in CFMMs, constructing price of anarchy and analyzing reordering MEV.
result Conditions under which reordering MEV shows logarithmic impact, and implications for MEV searchers and CFMM designers.
All DeFi markets are essentially CFMMs with increasing invariants.
problem Ensuring DeFi markets are free of arbitrage opportunities.
method Formalizing DeFi markets as CFMMs and proving the existence of increasing invariants.
result A DeFi market is arbitrage-free if and only if it has an increasing invariant.
The paper models blockchain queues and trading dynamics, finding conditions for transaction priority and price impact.
problem Understanding and predicting price impacts in blockchain trading environments.
method Developed a probabilistic model for blockchain queues with adversarial scheduling, derived expressions for transaction priority and price impact.
result Conditions for transaction priority and statistical models for price impact in blockchain trading environments.
This paper compares AMMs and LOBs in exchange mechanisms, formalizing complexity vs. expressiveness trade-offs.
problem Designing efficient exchange mechanisms between assets.
method Formalizes a complexity-approximation trade-off for CFMMs and LOBs, introducing an exchange complexity measure.
result Optimally expressive mechanisms can be designed with minimal complexity, allowing for arbitrary demand curves.
New formula identifies and quantifies costs for automated market makers.
problem Adverse selection costs faced by liquidity providers in automated market makers.
method Derives a Black-Scholes-like formula for AMMs and identifies loss-versus-rebalancing cost.
result Closed-form expressions for LVR applicable to all automated market makers.
This thesis studies CPMMs with CL, developing strategies for LTs and LPs.
problem Trading mechanisms and strategies for CPMMs with CL.
method Formalizes CPMMs with CL, develops strategies using market data and models.
result Derives optimal strategies for LTs and LPs in CPMMs with CL.
The paper examines statistical properties of IL and LVR in automated market makers.
problem Assessing the performance of automated market makers and their profitability.
method Analysis of random walk properties and statistical integral combined with CFMM mechanics.
result IL and LVR have identical expectation values but different distribution functions for Brownian motion.
PA-AMM divides reserves into active and passive parts for better liquidity provider wealth.
problem Reducing adverse selection costs in AMMs.
method Divides reserves into active and passive parts, rebalancing top of each block.
result Improves LP wealth compared to CFMMs by reducing LVR.
The paper develops a new framework for pricing and hedging liquidity in crypto markets.
problem Arbitrage and risk management in crypto market making.
method Developed a new mathematical framework using a coordinate system defined by price and intrinsic liquidity.
result Established a linear dependence of asset reserves and value functions on intrinsic liquidity, facilitating arbitrage-free pricing and delta hedging.