This research categorizes AMM designs for secure token exchanges.
problem Designing AMMs for cryptoeconomic systems can lead to financial risks and inefficiencies.
method Developed an AMM taxonomy and proposed three archetypes.
result AMM archetypes meet key requirements for token issuance and exchange.
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.
Blockchain-based exchanges adopt based on token pair volatility and personal use.
problem Token value loss and arbitrage issues in decentralized exchanges.
method Investigation of Automated Market Makers (AMMs) using transaction-level data.
result AMMs are adopted for high personal use or highly correlated token price movements.
This paper introduces a new metric to improve the performance of AMMs over centralised exchanges.
problem Lack of a precise metric to compare AMM performance with centralised exchanges.
method Introduces Rebalancing-versus-Rebalancing (RVR) to measure AMM performance more accurately.
result AMMs can offer superior execution and rebalancing efficiency compared to centralised exchanges, even with low fees.
Paper introduces CLVR to reduce price volatility in AMM exchanges.
problem Intra-block price volatility in AMM exchanges.
method CLVR constructs an ordering to minimize price volatility with low computation cost.
result CLVR minimizes price volatility with a small computation cost and can be externally verified.
This study interprets AMM fees as implied volatility, validating their relevance in digital asset markets.
problem Understanding the volatility of fees in decentralized exchange systems.
method Reinterpreting AMM fees as implied volatility and applying fixed-for-floating swaps to quote and validate these volatilities.
result The implied volatilities of digital assets can be accurately quoted using AMM fees, validating the approach.
QLAMMP optimizes fees on AMMs using Q-Learning.
problem Static AMMs cannot adapt to market changes, leading to high slippage.
method Developed a Q-Learning Agent (QLAMMP) to learn optimal fee rates.
result QLAMMP consistently outperforms static AMMs under various market conditions.
This paper addresses AMMs for expiring assets, ensuring liquidity and risk management.
problem AMMs struggle with assets that expire, leading to liquidity issues and risk exposure.
method Combines AMM and limit-order book features, ensuring liveness and dynamic price adjustment.
result A DEX for expiring assets maintains liquidity and risk management.
UAMM uses external market prices to improve AMM efficiency and reduce liquidity provider risk.
problem Traditional AMMs lack consideration of external markets and risk management.
method UAMM calculates prices by incorporating external market prices and impermanent loss, maintaining constant product curve properties.
result UAMM eliminates arbitrage opportunities when external market prices are efficient, reducing liquidity provider risk.
New dynamic curves improve cryptocurrency exchange liquidity.
problem Low liquidity and arbitrage opportunities in existing AMMs.
method Dynamic curves adjust AMM function based on market prices.
result Maintains liquidity and total LP value over wide market price ranges.
We introduce trading fees into AMM models and analyze their impact on swap rates and profits.
problem The impact of trading fees on AMM models and users' trading strategies.
method We extend a foundational AMM model by introducing a trading fee parameter and analyze the model using economic and mathematical rigor.
result Trading fees affect the additivity of swap rates and can lead to greater profits from larger trades.
A new AMM mechanism reduces losses and maximizes revenue from orderflows.
problem Reduces losses to informed orderflow and maximizes revenue from uninformed orderflow.
method Runs an onchain auction for pool manager role, allowing fee setting and price sensitivity.
result Proves higher liquidity in equilibrium compared to standard AMMs.
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 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.
A new AMM design reduces impermanent loss and retains more liquidity.
problem Inefficiencies in conventional AMM designs lead to liquidity loss and user engagement issues in DEXs.
method Proposes a dual-mechanism framework: a power-law invariant BMM and dynamic rebate system.
result Reduces impermanent loss by 36% and retains 3.98x more liquidity during price volatility.
Novel AMM model for pegged cryptoassets using nested OU processes.
problem Liquidity and risk management in markets for pegged cryptoassets.
method Multi-level nested Ornstein-Uhlenbeck (OU) processes for exchange rate dynamics, calibrated and filtered AMM model.
result Consistent efficient quotes and improved liquidity provision for pegged cryptoassets.
This paper optimizes liquidity provision in automated market makers using auction theory.
problem Optimizing profit for a monopolist liquidity provider in automated market makers.
method Introduces a Bayesian-like belief inference framework to model AMMs, characterizes profit-maximizing strategies using Myerson's optimal auction theory.
result Characterizes the optimal demand curve and payments for an IC AMM, revealing a bid-ask spread caused by asymmetry and monopoly pricing.
This study compares price discovery in ETH and BTC markets between centralized and decentralized exchanges.
problem Understanding price discovery dynamics in cryptocurrency markets.
method Comparative analysis of centralized and decentralized exchanges, using econometric tools.
result Centralized exchanges lead in ETH price discovery, while futures markets lead in BTC.
Optimal fees protect passive LPs in AMMs under varying market conditions.
problem Adverse selection losses in AMMs are not offset by static trading fees.
method Dynamic reduced-form model with parallel AMM and CEX, large-scale simulations, real market data analysis.
result Optimal AMM fees are stable under normal conditions but high in volatile periods to protect LPs.
Automated market-making for CBDCs and stable coins on blockchain.
problem Creating fair exchange rates for digital assets on blockchain.
method Developed an innovative approach for generating fair exchange rates.
result Illustrated the approach's efficacy on G-10 currency exchange rates.
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.
Privacy-preserving crypto exchanges adjust prices based on Gaussian noise.
problem Ensuring fair pricing in privacy-preserving cryptocurrency exchanges.
method Derive Kyle equilibrium with Gaussian noise perturbation, rescaling price-impact and strategy factors.
result Identify a privacy subsidy as a transfer from LP pool to traders, invariant to noise.
The Adversarially Learned Mixture Model (AMM) is a generative model for unsupervised or semi-supervised data clustering. The AMM is the first adversarially optimized method to model the conditional dependence between inferred continuous and categorical latent variables. Experiments on the MNIST and SVHN datasets show t…
This paper examines the quantitative finance aspects of AMMs in decentralized finance.
problem Understanding the mathematical and financial underpinnings of AMMs.
method Review of existing literature and analysis of mathematical aspects.
result Interesting relationship between AMMs and derivatives pricing and hedging.
The paper establishes axioms for AMMs to ensure fair pricing and fee structures.
problem Ensuring fair and efficient pricing in decentralized finance (DeFi) AMMs.
method Formulating axioms on utility functions to characterize swap sizes and pricing oracles.
result Most existing AMMs satisfy the proposed axioms, and a new AMM is proposed with desirable properties.
Walraswap solves batch auction pricing by finding optimal AMM swaps.
problem Executing all trade orders with optimal automated market makers (AMMs).
method Uses Brouwer's fixed-point theorem to find equilibrium prices.
result A solution to batch auction pricing problems in blockchain.
Enhances crypto-asset AMM with deep learning for better liquidity and efficiency.
problem Reduced slippage and improved liquidity in decentralized finance.
method Deep reinforcement learning for predicting market equilibrium and optimizing liquidity.
result Improved capital efficiency and reduced slippage for crypto-asset traders.
This study examines fees in AMMs to reduce losses from informed orderflow.
problem Minimizing losses from informed orderflow in AMMs.
method Modeling arbitrage dynamics and sensitivity to fee choices.
result Identified fees that mimic price directionality to reduce losses.
Continuous-time Kyle model shows privacy subsidy from noise-perturbed order flow.
problem Quantifying break-even fees for committed-AMM exchanges under privacy-aggregated information.
method Extended Nakamura's (2026) single-period result to continuous-time, observing order flow perturbed by Brownian noise.
result Cumulative privacy subsidy is identified as equivalent to Loss-Versus-Rebalancing in price observation gap.
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.
We refine toxicity bounds for dynamic liquidation incentives in CP-AMM systems.
problem Ensuring stability in dynamic liquidation incentives in automated market makers.
method Derived state-dependent toxicity bounds for dynamic liquidation incentives, reconciling them with CP-AMM price dynamics.
result State-dependent bounds and liquidity-depth-only condition for dynamic liquidation incentives.
New method finds better arbitrage opportunities in AMMs.
problem Finding optimal arbitrage trades in multi-token AMMs.
method Closed-form solutions using convex optimisation.
result Better arbitrage opportunities than traditional methods.
This paper studies how AMMs can minimize losses from arbitrage while retaining uninformed trading activity.
problem Minimizing losses from arbitrage in AMMs while retaining uninformed trading activity.
method Modeling arbitrage dynamics and sensitivity to fee choices, mapping to a random walk with a reward scheme.
result AMMs can maximize value retention by optimizing fee structures.
We analyze impermanent loss in AMMs and show G3Ms are simplest.
problem Understanding impermanent loss in automated market makers.
method Developed a general framework and analyzed Geometric Mean Market Makers (G3Ms).
result G3Ms have the simplest impermanent loss characteristics.
Triangle fees adjust fees based on trade size and price movement, improving price accuracy and revenue.
problem Price staleness and low fee revenue in AMMs.
method Decreasing marginal fees proportional to price movement, creating incentives for price accuracy.
result Triangle fees strictly improve the Pareto frontier of price accuracy versus losses.
Study shows AMM liquidity providers lose more than they earn, with varying profitability across pairs.
problem Arbitrage losses by liquidity providers on AMMs exceed fees earned.
method Empirical study of losses and profitability across different AMM pools and block times.
result Uniswap v2 pools are more profitable for passive LPs than Uniswap v3.
Developed concentrated liquidity in n-dimensional AMM with polar coordinates in Rust.
problem Risk of stacking too many stablecoin pools.
method Building concentrated liquidity positions with ticks in polar coordinates in Rust.
result Hedging risk of stacking stablecoin pools.
Decentralized prediction markets use AMMs to pool and withdraw liquidity, improving financial properties.
problem Creating a fair and efficient decentralized prediction market.
method Developed a liquidity-based AMM structure for prediction markets, studied liquidity management, and proposed trading fees.
result The decentralized AMM structure satisfies financial properties and can be managed with liquidity withdrawal.
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.
RAmmStein optimizes liquidity management in AMMs by learning to rebalance efficiently.
problem Optimal control of concentrated liquidity in decentralized exchanges.
method Formulates as an optimal control problem, uses Deep Reinforcement Learning with HJB-QVI.
result Achieves highest net ROI (1.60%) compared to greedy strategies, reduces rebalancing frequency by 85%.
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.
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.
FLAIR measures LP competitiveness in AMMs, improving LP performance evaluations.
problem LP returns are affected by both market risk and competitive strategies.
method Introduces FLAIR metric to quantify LP competitiveness and assesses its impact on LP returns.
result FLAIR captures dynamic behavior of LPs and differentiates between active provisioning strategies.
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.
Improved COD algorithm reduces streaming AMM errors and uses less space.
problem Efficiently approximate matrix multiplication with limited memory.
method Tighter error bound for COD, space optimality, sparse matrix variant.
result Improved COD is space optimal and more efficient for sparse matrices.
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.
Uniform AMMs control loss in prediction markets.
problem Controlling loss in prediction markets.
method Loss-versus-rebalancing (LVR) framework and uniform AMMs.
result Uniform AMMs achieve proportional LVR to pool value.
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.