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

Abstract

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