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研究生： 陳韋儒
Chen, Wei-Ru
論文名稱： 自動造市商機制與流動性提供者獎勵問題
A Study of AMM Mechanisms and Liquidity Provider Rewards
指導教授： 千野由喜
Chino, Yuki
東聖甯
Tung, Shen-Ning
口試委員: 陳隆奇
Chen, Lung Chi
陳冠宇
Chen, Guan Yu
學位類別： 碩士
Master
系所名稱： 理學院 - 數學系
Department of Mathematics
論文出版年： 2024
畢業學年度： 112
語文別： 英文
論文頁數： 49
中文關鍵詞： 自動造市商 、流動性提供者 、流動性池之價格模型 、機率與金融數學 、貝爾曼方程 、最佳停止問題
外文關鍵詞： Automated market maker, Liquidity provider, Liquidity pool price model, Probability theory and mathematical finance, Bellman equation, Optimal stopping problem
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    • 我們在這篇論文中分析了去中心化金融中的自動化做市商（AMMs），重點研究了Uniswap協議（V2和V3）[1,2]。我們形式化了交易和流動性提供機制，接著構建了一個由實證觀察支持的池子價格動態模型，並用其探討流動性提供者的預期收益與將初始資產存入銀行的比較，其中包含了根據現實數據推估的簡單數值結果。

    In this thesis, we analyze automated market makers (AMMs) in decentralized finance, focusing on the Uniswap protocol (V2 and V3) [1,2]. We formalize the trading and liquidity provision mechanisms, using them to construct a pool price dynamic justified by empirical observation. We then apply the model to investigate expected returns for liquidity providers compared with depositing initial assets to the bank, including some simple numerical results inffered from real data.

    Abstract i 1 Introduction 1 2 Uniswap V2 3 2.1 Uniswap V2 mechanism 3 2.1.1 Pool reserves curve and price 3 2.1.2 Trading Mechanism and Price Impact 4 2.1.3 Liquidity Provision and Impermanent Loss 5 2.1.4 Trading Fees 7 2.2 Price Dynamics Under Arbitrage Opportunities 8 2.2.1 Arbitrage 8 2.2.2 Price Process 12 2.3 LP reward problem 17 3 Uniswap V3 22 3.1 Uniswap V3 mechanism 22 3.1.1 Pool reserve curve and price 23 3.1.2 Trading Mechanism 26 3.1.3 Liquidity provision and Trading fee 27 3.1.4 Advantage of Uniswap V3 28 3.2 Price Dynamics Under Arbitrage Opportunities 29 3.3 LP return problem 30 3.3.1 Optimal stopping problem 32 3.3.2 Stop at boundary 40 3.3.3 Discussion 48 References 49

    [1] N. Z. Hayden Adams and D. Robinson, “Uniswap v2 core,” 2020.
    [2] M. S. Hayden Adams, Noah Zinsmeister, R. Keefer, and D. Robinson, “Uniswap v3 core,” 2021.
    [3] V. Mohan, “Automated market makers and decentralized exchanges: a defi primer,” Financial Innovation, vol. 8, p. 20, 02 2022.
    [4] M. D. Gould, M. A. Porter, S. Williams, M. McDonald, D. J. Fenn, and S. D. Howison,
    “Limit order books,” Quantitative Finance, vol. 13, pp. 1709–1742, November 2013.
    [5] M. Tassy and D. White, “Growth rate of a liquidity provider＇s wealth in xy = c automated market makers.,” 2020.
    [6] A. S. Goran Peskir, Optimal Stopping and Free-Boundary Problems. Birkhäuser Basel,2006.
    [7] R. C. Guillermo Angeris, Hsien-Tang Kao, C. Noyes, and T. Chitra, “An analysis of uniswap markets.,” Cryptoeconomic Systems, 2021.
    [8] B. A. Zhou Fan, Francisco Marmolejo-Cossío, H. Sun, X. Wang, and D. C. Parkes, “Dif-
    ferential liquidity provision in uniswap v3 and implications for contract design,” in ICAIF
    ’22: Proceedings of the Third ACM International Conference on AI in Finance, 2022.
    [9] U. R. Nicole Bäuerle, Markov Decision Processes with Applications to Finance. Springer
    Berlin, Heidelberg, 2021.

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