Constant Function Market Makers: Multi-Asset Trades via Convex Optimization

TL;DR

This paper demonstrates that multi-asset trades in constant function market makers (CFMMs) can be effectively formulated and solved as convex optimization problems, improving understanding and efficiency in decentralized exchanges.

Contribution

It introduces a convex optimization framework for multi-asset trades in CFMMs, enhancing the analysis and execution of complex trades in decentralized exchanges.

Findings

Multi-asset trade problems can be formulated as convex optimization problems.

Convex optimization provides reliable and efficient solutions for multi-asset trades.

This approach improves understanding and execution of complex trades in CFMM-based DEXs.

Abstract

The rise of Ethereum and other blockchains that support smart contracts has led to the creation of decentralized exchanges (DEXs), such as Uniswap, Balancer, Curve, mStable, and SushiSwap, which enable agents to trade cryptocurrencies without trusting a centralized authority. While traditional exchanges use order books to match and execute trades, DEXs are typically organized as constant function market makers (CFMMs). CFMMs accept and reject proposed trades based on the evaluation of a function that depends on the proposed trade and the current reserves of the DEX. For trades that involve only two assets, CFMMs are easy to understand, via two functions that give the quantity of one asset that must be tendered to receive a given quantity of the other, and vice versa. When more than two assets are being exchanged, it is harder to understand the landscape of possible trades. We observe that various problems of choosing a multi-asset trade can be formulated as convex optimization problems, and can therefore be reliably and efficiently solved.