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Within this work we consider an axiomatic framework for Automated MarketMakers (AMMs). By imposing reasonable axioms on the underlying utilityfunction, we are able to characterize the properties of the swap size of theassets and of the resulting pricing oracle. In providing these general AMMaxioms, we define a novel measure of price impacts that can be used to quantifythose costs between different constructions. We have analyzed many existingAMMs and shown that the vast majority of them satisfy our axioms. We have alsoconsidered the question of fees and divergence loss. In doing so, we haveproposed a new fee structure so as to make the AMM indifferent to transactionsplitting. Finally, we have proposed a novel AMM that has nice analyticalproperties and provides a large range over which there is no divergence loss.

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