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

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  • Maxim Bichuch
  • Zachary Feinstein

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.

Suggested Citation

  • Maxim Bichuch & Zachary Feinstein, 2022. "Axioms for Automated Market Makers: A Mathematical Framework in FinTech and Decentralized Finance," Papers 2210.01227, arXiv.org, revised Sep 2024.
    • Handle: RePEc:arx:papers:2210.01227
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    File URL: http://arxiv.org/pdf/2210.01227
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    References listed on IDEAS

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    1. Guillermo Angeris & Tarun Chitra, 2020. "Improved Price Oracles: Constant Function Market Makers," Papers 2003.10001, arXiv.org, revised Jun 2020.
    2. Alex Lipton & Artur Sepp, 2021. "Automated Market-Making for Fiat Currencies," Papers 2109.12196, arXiv.org.
    3. Guillermo Angeris & Akshay Agrawal & Alex Evans & Tarun Chitra & Stephen Boyd, 2021. "Constant Function Market Makers: Multi-Asset Trades via Convex Optimization," Papers 2107.12484, arXiv.org.
    4. Guillermo Angeris & Alex Evans & Tarun Chitra, 2021. "Replicating Market Makers," Papers 2103.14769, arXiv.org.
    5. Jun Deng & Hua Zong & Yun Wang, 2022. "Static Replication of Impermanent Loss for Concentrated Liquidity Provision in Decentralised Markets," Papers 2205.12043, arXiv.org, revised Mar 2023.
    6. Agostino Capponi & Ruizhe Jia, 2021. "The Adoption of Blockchain-based Decentralized Exchanges," Papers 2103.08842, arXiv.org, revised Jul 2021.
    7. Harold Demsetz, 1968. "The Cost of Transacting," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 82(1), pages 33-53.
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    Citations

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    Cited by:

    1. Peplluis R. Esteva & Alberto Ballesteros Rodr'iguez, 2023. "Invoice discounting using kelly criterion by automated market makers-like implementations," Papers 2302.09009, arXiv.org.
    2. Roger Lee, 2023. "All AMMs are CFMMs. All DeFi markets have invariants. A DeFi market is arbitrage-free if and only if it has an increasing invariant," Papers 2310.09782, arXiv.org, revised Dec 2023.
    3. Georg Menz & Moritz Vo{ss}, 2023. "Aggregation of financial markets," Papers 2309.04116, arXiv.org, revised Sep 2024.
    4. Hamed Amini & Maxim Bichuch & Zachary Feinstein, 2023. "Decentralized Prediction Markets and Sports Books," Papers 2307.08768, arXiv.org, revised May 2024.
    5. Jason Milionis & Ciamac C. Moallemi & Tim Roughgarden, 2023. "Complexity-Approximation Trade-offs in Exchange Mechanisms: AMMs vs. LOBs," Papers 2302.11652, arXiv.org, revised Apr 2023.
    6. Peplluis R. Esteva & Andrés El-Fakdi & Alberto Ballesteros-Rodríguez, 2023. "Invoice Discounting Using Kelly Criterion by Automated Market Makers-like Implementations," Mathematics, MDPI, vol. 11(7), pages 1-37, March.
    7. Kenan Wood & Maurice Herlihy & Hammurabi Mendes & Jonad Pulaj, 2024. "Expiring Assets in Automated Market Makers," Papers 2401.04289, arXiv.org.
    8. Sergey Goncharov & Andrey Nechesov, 2023. "Axiomatization of Blockchain Theory," Mathematics, MDPI, vol. 11(13), pages 1-16, July.

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