Adaptive Curves for Optimally Efficient Market Making

ArXiv ID: 2406.13794 “View on arXiv”

Authors: Unknown

Abstract

Automated Market Makers (AMMs) are essential in Decentralized Finance (DeFi) as they match liquidity supply with demand. They function through liquidity providers (LPs) who deposit assets into liquidity pools. However, the asset trading prices in these pools often trail behind those in more dynamic, centralized exchanges, leading to potential arbitrage losses for LPs. This issue is tackled by adapting market maker bonding curves to trader behavior, based on the classical market microstructure model of Glosten and Milgrom. Our approach ensures a zero-profit condition for the market maker’s prices. We derive the differential equation that an optimal adaptive curve should follow to minimize arbitrage losses while remaining competitive. Solutions to this optimality equation are obtained for standard Gaussian and Lognormal price models using Kalman filtering. A key feature of our method is its ability to estimate the external market price without relying on price or loss oracles. We also provide an equivalent differential equation for the implied dynamics of canonical static bonding curves and establish conditions for their optimality. Our algorithms demonstrate robustness to changing market conditions and adversarial perturbations, and we offer an on-chain implementation using Uniswap v4 alongside off-chain AI co-processors.

Keywords: Automated Market Maker (AMM), Market Microstructure, Bonding Curves, Kalman Filtering, Zero-Profit Condition, Cryptocurrency/DeFi

Complexity vs Empirical Score

• Math Complexity: 8.0/10
• Empirical Rigor: 6.5/10
• Quadrant: Holy Grail
• Why: The paper employs advanced mathematical techniques like differential equations, stochastic models, and Kalman filtering, which is dense and complex. However, it includes robust theoretical comparisons, on-chain implementation with Uniswap v4, and adversarial robustness analysis, making it highly data/implementation-focused.

  flowchart TD
    A["Research Goal"] -->|Formulate| B["Adaptive Bonding Curves"]
    B -->|Methodology| C["Market Microstructure Model<br>Glosten-Milgrom"]
    C -->|Core Condition| D["Zero-Profit Condition"]
    D -->|Mathematical Form| E["Optimality Differential Equation"]
    E -->|Solve Using| F["Computational Process<br>Kalman Filtering"]
    F -->|Data Inputs| G["Off-chain AI Co-processors<br>No Price Oracles"]
    G -->|Implementation| H["On-chain: Uniswap v4"]
    H -->|Key Outcomes| I["Minimized Arbitrage Loss &<br>Adaptive Liquidity"]