Geometric Mean Market Maker

Growth rate of liquidity provider’s wealth in G3Ms ArXiv ID: 2403.18177 “View on arXiv” Authors: Unknown 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. ...

Closed-form solutions for generic N-token AMM arbitrage ArXiv ID: 2402.06731 “View on arXiv” Authors: Unknown Abstract Convex optimisation has provided a mechanism to determine arbitrage trades on automated market markets (AMMs) since almost their inception. Here we outline generic closed-form solutions for $N$-token geometric mean market maker pool arbitrage, that in simulation (with synthetic and historic data) provide better arbitrage opportunities than convex optimisers and is able to capitalise on those opportunities sooner. Furthermore, the intrinsic parallelism of the proposed approach (unlike convex optimisation) offers the ability to scale on GPUs, opening up a new approach to AMM modelling by offering an alternative to numerical-solver-based methods. The lower computational cost of running this new mechanism can also enable on-chain arbitrage bots for multi-asset pools. ...