Growth rate of liquidity provider's wealth in G3Ms
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910119826030592 |
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| author | Lee, Cheuk Yin Tung, Shen-Ning Wang, Tai-Ho |
| author_facet | Lee, Cheuk Yin Tung, Shen-Ning Wang, Tai-Ho |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_18177 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Growth rate of liquidity provider's wealth in G3Ms Lee, Cheuk Yin Tung, Shen-Ning Wang, Tai-Ho Mathematical Finance Pricing of Securities Trading and Market Microstructure 91G15 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. |
| title | Growth rate of liquidity provider's wealth in G3Ms |
| topic | Mathematical Finance Pricing of Securities Trading and Market Microstructure 91G15 |
| url | https://arxiv.org/abs/2403.18177 |