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

Automated Market Makers (AMMs) are smart contracts that have emerged as a cornerstone of Decentralized Finance (DeFi), replacing traditional intermediaries for trading digital assets. However, the underlying principles, risks, and economic properties of these novel markets require a rigorous mathematical foundation. In “Axioms for automated market makers: A mathematical framework in fintech and decentralized finance,” Maxim Bichuch and Zachary Feinstein construct such a foundation. The authors propose a set of intuitive axioms for the utility functions that govern AMMs. From this framework, they characterize the resulting swap and pricing properties and define a novel measure of price impact to quantify and compare transaction costs across different AMM designs. The work also addresses practical issues by proposing a new fee structure that ensures indifference to transaction splitting and analyzing the critical risk of divergence loss for liquidity providers, offering a comprehensive guide for designing and analyzing these new financial technologies.