Paper proposes efficient cost functions for automated market makers in DeFi.
problem Inefficient and computationally complex cost functions in DeFi.
method Proposes and analyzes constant circle/ellipse based cost functions.
result Proposed cost functions are computationally efficient and robust against attacks.
This paper mixes constant sum and constant product market makers to improve their features.
problem Improving the balance between stable exchange rates and liquidity in automated market makers.
method Mixing and designing new methods for AMMs with specific features.
result Demonstrates new tools for creating markets with desired characteristics.
This paper analyzes and compares different Automated Market Maker mechanisms.
problem Impermanent loss in Constant Function Market Makers.
method Mean-Variance analysis of liquidity providers' profit and loss, comparison of different mechanisms.
result Optimized oracle-based mechanisms outperform Constant Function Market Makers.
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.
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.
Optimal dynamic fees found for AMMs to deter arbitrageurs and attract noise traders.
problem Optimizing fees in AMMs to balance against arbitrage and noise trading.
method Approximate closed-form solutions to control problem, study of fee structure.
result Two distinct fee regimes identified: high fees to deter arbitrage, low fees to attract noise traders.
Framework to generalize impermanent loss for decentralized exchanges.
problem Difficult analysis of impermanent loss due to diverse market maker algorithms and fee structures.
method Developed a framework to generalize impermanent loss for constant function market makers with optional concentrated liquidity.
result Identified conditions for profitability of liquidity provisioning.
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 study optimizes crypto-market trading conditions without assuming convexity.
problem Optimizing crypto-market trading conditions without convexity.
method Rigorous mathematical analysis of constant function market makers under quasilinear trade functions.
result Quasilinear trade functions can replicate convex functions' robustness against arbitrage.
Optimizes liquidity provision in decentralized exchanges with utility indifference market makers.
problem Impermanent loss in decentralized exchanges without transaction fees.
method Mathematical formulation of liquidity provision, focusing on utility indifference market makers.
result No-arbitrage conditions and optimal arbitrage strategies are established.
New metric to measure liquidity position PNL, delta hedging algorithm for automated market makers.
problem Vulnerability of liquidity positions to price changes in underlying assets.
method Proposes a new metric for measuring PNL, delta hedging algorithm for various AMMs.
result New metric more accurately measures net value change due to price movement.
New automated market makers for multi-asset trading.
problem Liquidity management in multi-asset trading.
method Derived from self-financing transactions and rebalancing principles.
result Constant product market maker as a special case.
This paper examines the uniform properties of AMMs in cryptocurrency markets.
problem Theoretical uniformity of AMMs despite diverse strategies.
method Derives a universal formula for liquidity provisioning and compares models.
result Constant function and token swap models are equivalent under uniform liquidity.
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.
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.
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.
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 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.
Geometric Mean Market Makers super-hedge impermanent loss without models.
problem Super-hedging impermanent loss in Geometric Mean Market Makers.
method Model-free rebalancing strategy.
result Loss-versus-rebalancing vanishes due to finite variation exchange rate.
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.
Paper analyzes constant-product market making protocols.
problem Understanding and optimizing constant-product market making.
method Mathematical analysis of trade splitting and fee recompounding.
result Splitting trades does not affect final exchange rate.
The profitability of CPMMs is significantly impacted by mint and burn fees.
problem Understanding the profitability of decentralized exchanges.
method Formalized liquidity providers' profitability conditions, studied the effect of mint and burn fees, and compiled a large data set from Uniswap V2 transactions.
result The profitability of liquidity provision is severely affected by mint and burn costs.
Study optimizes market making in Chinese stock market with stochastic control and scenario analysis.
problem Limited research on market making in Chinese stock market.
method Optimal market making framework with exponential CARA utility function, accounting for market conditions and risks.
result Impact of volatility and stamp duty on market maker's profit and liquidity.
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.
This paper examines MEV attacks in dynamic AMMs and proposes new protections.
problem Dynamic AMMs introduce new MEV attack vectors due to inter-block weight changes.
method Analyzed inter-block weight changes as analogous to trades, conducted simulations.
result New inter-block protections are required to guard against multi-block MEV attacks.
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.
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.
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.
Modeling price dynamics in AMMs with fees using geometric Brownian motion.
problem Understanding price dynamics in AMMs with transaction fees.
method Geometric Brownian motion, local times, excursion theory.
result Derivation of time-changed representation and limiting behavior of AMM prices.
We introduce a class of utility-based market makers that always accept orders at their risk-neutral prices. We derive necessary and sufficient conditions for such market makers to have bounded loss. We prove that hyperbolic absolute risk aversion utility market makers are equivalent to weighted pseudospherical scoring …
Derives pricing formulas for liquidity tokens in CPMMs, showing riskless growth.
problem Liquidity token pricing and hedging in CPMMs.
method Derives risk-neutral pricing and hedging formulas for CPMM liquidity tokens using derivative pricing perspective.
result Shows that hedging CPMM liquidity tokens should grow at the risk-free rate, contradicting empirical observations.
This research compiles knowledge on decentralized exchanges with AMM protocols.
problem Improving and developing AMM-based decentralized exchanges.
method Established a general AMM framework, compared mechanics, discussed security and privacy.
result Illustrated conservation and slippage functions of AMM protocols.
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.
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.
Paper calculates greeks for DeFi LPs and introduces Impermanent Gain.
problem Liquidity Providers in DeFi are exposed to Impermanent Loss.
method Tailored Black & Scholes formulas for DeFi markets.
result Introduced Impermanent Gain for risk management.
We introduce a modular framework for market making. It combines cost-function based automated market makers with bandit algorithms. We obtain worst-case profits guarantee's relative to the best in hindsight within a class of natural "overround" cost functions . This combination allow us to have distribution-free guaran…
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.
Modeling market makers' quoting strategies to understand price impact.
problem Understanding how price impact arises from market makers' quoting strategies.
method Modeling market making as a dynamic auction using Stochastic Differential Games and finding Nash Equilibrium.
result The price impact function derived from market makers' strategies matches the Almgren-Chriss model.
Model shows phase transitions in asset pricing with market maker incentives.
problem Analyzing asset pricing with market maker profit incentives.
method Stochastic game theory, neural networks.
result Equilibrium experiences three phases: linear pricing, mid-price with spread, and metastable state.
Derives a size premium from automated market makers in decentralized AI subnets.
problem Determining the profitability and risk of decentralized AI subnets.
method Analyzes daily data on 128 subnets, tests the size premium, and calculates transaction costs.
result The size premium is reduced by a halving of token emissions but remains profitable only below a certain asset threshold.
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.
Optimizes routing in decentralized exchanges with gas fees.
problem Routing in decentralized exchanges with fixed gas fees.
method General optimization framework with mixed-integer model, incorporating gas fees.
result Explicit Karush-Kuhn-Tucker system linking prices, fees, and activation.
This paper models AMM positions using CI options to calculate LVR and provide actionable guidance.
problem Calculating and managing adverse-selection costs in automated market makers (AMMs).
method Modeling AMM positions as perpetual American CI options to replicate delta and calculate LVR.
result LVR is identical to theta of CI options, and AMM positions have approximately constant LVR over long windows.
Study liquidity provision with exogenous competition using a reference market maker.
problem Liquidity provision in the presence of exogenous competition.
method Model a reference market maker who optimizes posted depths, competing market makers using a rule of thumb.
result Model admits approximate closed-form solution for a linear-quadratic goal functional.
We develop a single-period model for a large economic agent who trades with market makers at their utility indifference prices. A key role is played by a pair of conjugate saddle functions associated with the description of Pareto optimal allocations in terms of the utility function of a representative market maker.
Optimal design of automated market makers for decentralized exchanges.
problem Maximizing utility for liquidity providers in decentralized exchanges.
method Modeling a risk-averse liquidity provider's optimal strategy and the optimal design of automated market makers.
result The optimal unit trading fee increases with asset volatility.
This study optimizes trading and arbitrage in decentralized finance's CPMs, revealing convexity costs and developing efficient strategies.
problem Optimizing trading and arbitrage in decentralized finance's constant product markets (CPMs).
method Developed models for CPMs in competing centralised exchanges, CPMs, and both venues. Derived computationally efficient strategies.
result Accurately estimated convexity costs in CPMs, which are linear in trade size and nonlinear in liquidity depth and exchange rate.
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.