Paper: arXiv 2404.13291

Authors: Xue Dong He, Chen Yang, Yutian Zhou

Abstract

Automated market makers are a popular mechanism used on decentralized exchange, through which users trade assets with each other directly and automatically through a liquidity pool and a fixed pricing function. The liquidity provider contributes to the liquidity pool by supplying assets to the pool, and in return, they earn trading fees from investors who trade in the pool. We propose a model of optimal liquidity provision in which a risk-averse liquidity provider decides the amount of wealth she would invest in the decentralized market to provide liquidity in a two-asset pool, trade in a centralized market, and consume in multiple periods. We derive the liquidity provider’s optimal strategy and the optimal design of the automated market maker that maximizes the liquidity provider’s utility. We find that the optimal unit trading fee increases in the volatility of the fundamental exchange rate of the two assets. We also find that the optimal pricing function is chosen to make the asset allocation in the liquidity pool efficient for the liquidity provider.

Complexity vs Empirical Score

  • Math Complexity: 7.5/10
  • Empirical Rigor: 2.5/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents a rigorous theoretical framework using multi-period utility maximization to solve for optimal liquidity provision and fee structures in AMMs. However, it is purely theoretical with minimal empirical backtesting or real-world transaction data validation.

Research Flowchart

  flowchart TD
    A[Research Goal: Optimal AMM Design & Liquidity Provision Strategy] --> B[Inputs: Asset Volatility, Fee Rate, Risk Aversion & Multi-period Consumption]
    B --> C[Methodology: Utility Maximization Model for Risk-Averse LP]
    C --> D[Computational Optimization: Balance DEX Pool, Centralized Trading & Consumption]
    D --> E[Outcome 1: Optimal trading fee increases with exchange rate volatility]
    D --> F[Outcome 2: Optimal pricing function ensures efficient asset allocation]

Cited References (49)

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and 41 more
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2 of 49 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.