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Constant Function Market Makers: Multi-Asset Trades via Convex Optimization

Author

Listed:
  • Guillermo Angeris
  • Akshay Agrawal
  • Alex Evans
  • Tarun Chitra
  • Stephen Boyd

Abstract

The rise of Ethereum and other blockchains that support smart contracts has led to the creation of decentralized exchanges (DEXs), such as Uniswap, Balancer, Curve, mStable, and SushiSwap, which enable agents to trade cryptocurrencies without trusting a centralized authority. While traditional exchanges use order books to match and execute trades, DEXs are typically organized as constant function market makers (CFMMs). CFMMs accept and reject proposed trades based on the evaluation of a function that depends on the proposed trade and the current reserves of the DEX. For trades that involve only two assets, CFMMs are easy to understand, via two functions that give the quantity of one asset that must be tendered to receive a given quantity of the other, and vice versa. When more than two assets are being exchanged, it is harder to understand the landscape of possible trades. We observe that various problems of choosing a multi-asset trade can be formulated as convex optimization problems, and can therefore be reliably and efficiently solved.

Suggested Citation

  • 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.
    • Handle: RePEc:arx:papers:2107.12484
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    File URL: http://arxiv.org/pdf/2107.12484
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    References listed on IDEAS

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    2. Nicholas Moehle & Enzo Busseti & Stephen Boyd & Matt Wytock, 2019. "Dynamic Energy Management," Springer Optimization and Its Applications, in: Jesús M. Velásquez-Bermúdez & Marzieh Khakifirooz & Mahdi Fathi (ed.), Large Scale Optimization in Supply Chains and Smart Manufacturing, pages 69-126, Springer.
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    12. Guillermo Angeris & Alex Evans & Tarun Chitra, 2021. "Replicating Market Makers," Papers 2103.14769, arXiv.org.
    13. Brendan O’Donoghue & Eric Chu & Neal Parikh & Stephen Boyd, 2016. "Conic Optimization via Operator Splitting and Homogeneous Self-Dual Embedding," Journal of Optimization Theory and Applications, Springer, vol. 169(3), pages 1042-1068, June.
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    Cited by:

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    4. Maxim Bichuch & Zachary Feinstein, 2022. "Axioms for Automated Market Makers: A Mathematical Framework in FinTech and Decentralized Finance," Papers 2210.01227, arXiv.org, revised Feb 2025.
    5. Hamed Amini & Maxim Bichuch & Zachary Feinstein, 2023. "Decentralized Prediction Markets and Sports Books," Papers 2307.08768, arXiv.org, revised Jan 2025.
    6. Philippe Bergault & Louis Bertucci & David Bouba & Olivier Gu'eant, 2022. "Automated Market Makers: Mean-Variance Analysis of LPs Payoffs and Design of Pricing Functions," Papers 2212.00336, arXiv.org, revised Nov 2023.
    7. Guillermo Angeris & Tarun Chitra & Alex Evans & Stephen Boyd, 2022. "Optimal Routing for Constant Function Market Makers," Papers 2204.05238, arXiv.org.
    8. Guillermo Angeris & Alex Evans & Tarun Chitra, 2021. "Replicating Monotonic Payoffs Without Oracles," Papers 2111.13740, arXiv.org.

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