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An arbitrage driven price dynamics of Automated Market Makers in the presence of fees

Author

Listed:
  • Joseph Najnudel
  • Shen-Ning Tung
  • Kazutoshi Yamazaki
  • Ju-Yi Yen

Abstract

We present a model for price dynamics in the Automated Market Makers (AMM) setting. Within this framework, we propose a reference market price following a geometric Brownian motion. The AMM price is constrained by upper and lower bounds, determined by constant multiplications of the reference price. Through the utilization of local times and excursion-theoretic approaches, we derive several analytical results, including its time-changed representation and limiting behavior.

Suggested Citation

  • Joseph Najnudel & Shen-Ning Tung & Kazutoshi Yamazaki & Ju-Yi Yen, 2024. "An arbitrage driven price dynamics of Automated Market Makers in the presence of fees," Papers 2401.01526, arXiv.org.
    • Handle: RePEc:arx:papers:2401.01526
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    File URL: http://arxiv.org/pdf/2401.01526
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    References listed on IDEAS

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    1. Jason Milionis & Ciamac C. Moallemi & Tim Roughgarden, 2023. "Automated Market Making and Arbitrage Profits in the Presence of Fees," Papers 2305.14604, arXiv.org.
    2. Agostino Capponi & Ruizhe Jia, 2021. "The Adoption of Blockchain-based Decentralized Exchanges," Papers 2103.08842, arXiv.org, revised Jul 2021.
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    Cited by:

    1. Wei-Ru Chen & A. Christian Silva & Shen-Ning Tung, 2024. "Stylized facts in Web3," Papers 2408.07653, arXiv.org, revised Aug 2024.

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