Paper: arXiv 2402.06731

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.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 3.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents advanced mathematical derivations for closed-form solutions using Lagrange multipliers and introduces a trade signature concept for N-token pools, indicating high mathematical complexity. However, the empirical validation relies on synthetic simulations and lacks backtest-ready code, datasets, or real-world implementation details, resulting in low empirical rigor.

Research Flowchart

  flowchart TD
  A["Research Goal: Find closed-form solutions<br>for N-token AMM arbitrage"] --> B["Methodology: Derive generic equations<br>for Geometric Mean Market Maker"]
  
  B --> C{"Data / Inputs"}
  C --> D1["Synthetic Data"]
  C --> D2["Historic Market Data"]
  C --> D3["AMM Pool Parameters<br>e.g., constant product k"]
  
  D1 & D2 & D3 --> E["Computational Process:<br>Parallel GPU Execution"]
  E --> F["Comparison: Closed-form vs.<br>Convex Optimization Solvers"]
  
  F --> G{"Key Findings / Outcomes"}
  G --> H1["Better arbitrage opportunities<br>identified"]
  G --> H2["Capitalises on opportunities<br>sooner (faster execution)"]
  G --> H3["Lower computational cost<br>enables on-chain bots"]

Cited References (18)

  1. Temporal-Function Market Making (2023)
  2. Temporal-Function Market Making Litepaper (2023) — link
  3. QuantAMM Whitepaper (2023)
  4. Uniswap v2 core (2020)
  5. Uniswap v3 core (2021)
  6. KyberSwap: Dynamic Automated Market Making (2021)
  7. Balancer: A non-custodial portfolio manager, liquidity provider, and price sensor. (2019)
  8. When does the tail wag the dog? Curvature and market making (2020) — link
and 10 more
  1. An analysis of Uniswap markets (2021) — link
  2. Liquidity Provider Returns in Geometric Mean Markets (2019) — link
  3. Automated Market Making and Loss-Versus-Rebalancing (2022) — link
  4. Automated Market Making and Loss-Versus-Rebalancing (2021) — link
  5. Ethereum Block Times, MEV, and LP returns (2022) — link
  6. Fast Approximation of the Lambert W Function for Virtual Analog Modelling (2019)
  7. A Sequence of Series for the Lambert W Function (1997) — link
  8. Constant Function Market Makers: Multi-Asset Trades via Convex Optimization (2021) — link
  9. Optimal Routing for Constant Function Market Makers (2022) — link
  10. An Efficient Algorithm for Optimal Routing Through Constant Function Market Makers (2023) — link

0 of 18 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.