Adaptive Curves for Optimally Efficient Market Making

TL;DR

This paper introduces an adaptive bonding curve approach for Automated Market Makers in DeFi, minimizing arbitrage losses by dynamically adjusting to market conditions without relying on external price oracles.

Contribution

It develops a differential equation-based method for optimal adaptive curves, leveraging Kalman filtering and on-chain implementation, enhancing AMM efficiency and robustness.

Findings

Achieves zero-profit condition for market makers.

Effectively estimates external market prices without oracles.

Demonstrates robustness to market changes and adversarial attacks.

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.