Axioms for Automated Market Makers: A Mathematical Framework in FinTech and Decentralized Finance

Within this work we consider an axiomatic framework for Automated Market Makers (AMMs). AMMs are smart contracts that set prices for swaps on a pool of assets. By imposing reasonable axioms on the underlying utility function, we are able to characterize the properties of the swap size of the assets and of the resulting pricing oracle. In providing these general axioms, we define a novel measure of price impacts that can be used to quantify those costs between different AMM constructions. We have analyzed many existing AMMs and shown that the vast majority of them satisfy our axioms. We have also considered the question of fees and divergence loss. In doing so, we have proposed a new fee structure so as to make the AMM indifferent to transaction splitting. Finally, we have proposed a novel AMM that has nice analytical properties and provides a large range over which there is no divergence loss.

Funding: M. Bichuch was partially supported by the NSF, Division of Mathematical Sciences [Grant DMS-1736414]. M. Bichuch and Z. Feinstein were both partially supported by the Stellar Development Foundation Academic Research Grants program.

Supplemental Material: All supplemental materials, including the code, data, and files required to reproduce the results, are available at https://doi.org/10.1287/opre.2022.0520.