Paper: arXiv 2610.21057

Authors: Masaaki Fukasawa

Abstract

We study liquidity provision in automated market makers when trading in the external market incurs proportional transaction costs. We consider both separately collected fees and fees retained in reserves. The benchmark is a self-financing strategy holding the same total risky inventory and trading at the external bid and ask. Under continuous external prices and pure arbitrage, the pool and benchmark have identical liquidation wealth whenever the pool fee or the external spread is positive. Thus loss-versus-rebalancing relative to this transaction-cost benchmark is zero, even without a pool fee if the external spread is positive. We then construct retained-fee utility-indifference pools that implement admissible decreasing inventory schedules, and geometric mean pools that implement feasible constant no-trade boundaries for portfolio weights. These results offer an investment interpretation of liquidity provision: by choosing the pool design, a liquidity provider can specify a trading strategy whose rebalancing is carried out by arbitrageurs.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 2.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents a highly mathematical and theoretical analysis of AMM liquidity provision under transaction costs, with detailed derivations and propositions. While the theoretical framework is novel and well-developed, there is no empirical validation or backtesting presented in the excerpt, placing it firmly in the ‘Lab Rats’ quadrant. The clarity is good for a technical paper, but reproducibility is limited by the lack of explicit code or data.

Research Flowchart

  flowchart TD
    A[Research Goal: Study Liquidity Provision in AMMs with External Proportional Transaction Costs] --> B{Methodology: Benchmark Self-Financing Strategy};
    B --> C[Inputs: Continuous External Prices, Pure Arbitrage, Pool Fees/External Spread];
    C --> D{Computational Process: Comparative Analysis of Pool vs. Benchmark Liquidation Wealth};
    D --> E[Key Finding 1: LVR is Zero if Pool Fee or External Spread > 0];
    E --> F[Key Finding 2: Utility-Indifference Pools for Decreasing Inventory, Geometric Mean Pools for Constant No-Trade Boundaries];
    F --> G[Outcome: Investment Interpretation - LP Specifies Trading Strategy Carried Out by Arbitrageurs];