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

TL;DR

This paper develops an axiomatic framework for Automated Market Makers (AMMs) in FinTech and DeFi, characterizing their properties, proposing new measures for price impact, and introducing innovative fee structures and AMM designs.

Contribution

It introduces a comprehensive axiomatic approach to analyze AMMs, proposes a new measure of price impact, and designs a novel AMM with minimal divergence loss.

Findings

Most existing AMMs satisfy the proposed axioms

A new fee structure makes AMMs indifferent to transaction splitting

A novel AMM design offers large divergence loss-free range

Abstract

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.