Growth rate of liquidity provider's wealth in G3Ms

[2403.18177] Growth rate of liquidity provider's wealth in G3Ms Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Quantitative Finance > Mathematical Finance arXiv:2403.18177 (q-fin) [Submitted on 27 Mar 2024 ( v1 ), last revised 11 Apr 2026 (this version, v4)] Title: Growth rate of liquidity provider's wealth in G3Ms Authors: Cheuk Yin Lee , Shen-Ning Tung , Tai-Ho Wang View a PDF of the paper titled Growth rate of liquidity provider's wealth in G3Ms, by Cheuk Yin Lee and 2 other authors View PDF HTML (experimental) Abstract: We study how trading fees and continuous-time arbitrage affect the profitability of liquidity providers (LPs) in Geometric Mean Market Makers (G3Ms). We use stochastic reflected diffusion processes to analyze the dynamics of a G3M model under the arbitrage-driven market. Our research focuses on calculating LP wealth and extends the findings of Tassy and White related to the constant product market maker (Uniswap v2) to a wider range of G3Ms, including Balancer. This allows us to calculate the long-term expected logarithmic growth of LP wealth, offering new insights into the complex dynamics of AMMs and their implications for LPs in decentralized finance. Comments: 42 pages, 5 figures Subjects: Mathematical Finance (q-fin.MF) ; Pricing of Securities (q-fin.PR); Trading and Market Microstructure (q-fin.TR) MSC classes: 91G15 Cite as: arXiv:2403.18177 [q-fin.MF] (or arXiv:2403.18177v4 [q-fin.MF] for this version) https://doi.org/10.48550/arXiv.2403.18177 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Shen-Ning Tung [ view email ] [v1] Wed, 27 Mar 2024 01:10:31 UTC (30 KB) [v2] Wed, 8 Jan 2025 17:55:44 UTC (1,322 KB) [v3] Sat, 6 Sep 2025 22:58:15 UTC (1,278 KB) [v4] Sat, 11 Apr 2026 11:36:22 UTC (1,166 KB) Full-text links: Access Paper: View a PDF of the paper titled Growth rate of liquidity provider's wealth in G3Ms, by Cheuk Yin Lee and 2 other authors View PDF HTML (experimental) TeX Source view license Current browse context: q-fin.MF < prev | next > new | recent | 2024-03 Change to browse by: q-fin q-fin.PR q-fin.TR References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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