2024/03/27 by Lee, Cheuk Yin, Tung, Shen-Ning, Wang, Tai-Ho
#91G15 #FOS: Economics and business #Mathematical Finance (q-fin.MF) #Pricing of Securities (q-fin.PR) #Trading and Market Microstructure (q-fin.TR)
paper · doi:10.48550/arxiv.2403.18177
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.