Equilibrium Liquidity and Risk Offsetting in Decentralised Markets

ArXiv ID: 2512.19838 “View on arXiv”

Authors: Fayçal Drissi, Xuchen Wu, Sebastian Jaimungal

Abstract

We develop an economic model of decentralised exchanges (DEXs) in which risk-averse liquidity providers (LPs) manage risk in a centralised exchange (CEX) based on preferences, information, and trading costs. Rational, risk-averse LPs anticipate the frictions associated with replication and manage risk primarily by reducing the reserves supplied to the DEX. Greater aversion reduces the equilibrium viability of liquidity provision, resulting in thinner markets and lower trading volumes. Greater uninformed demand supports deeper liquidity, whereas higher fundamental price volatility erodes it. Finally, while moderate anticipated price changes can improve LP performance, larger changes require more intensive trading in the CEX, generate higher replication costs, and induce LPs to reduce liquidity supply.

Keywords: Decentralized Exchanges (DEX), Liquidity Provision, Market Microstructure, Risk Management, Arbitrage, Cryptocurrency/DeFi

Complexity vs Empirical Score

• Math Complexity: 9.0/10
• Empirical Rigor: 2.0/10
• Quadrant: Lab Rats
• Why: The paper employs advanced stochastic control, forward-backward stochastic differential equations (FBSDEs), differential Riccati equations, and variational methods, indicating very high mathematical complexity. However, it is purely theoretical with no backtests, datasets, or implementation details, resulting in low empirical rigor.

  flowchart TD
    R["Research Goal<br>Liquidity in Decentralized Exchanges"] --> M["Methodology<br>Rational Risk-Averse LP Model"]
    M --> I["Key Inputs<br>Risk Aversion, Volatility, Demand"]
    I --> C["Computational Process<br>Cost-Benefit Analysis & Optimization"]
    C --> F["Key Findings<br>Thinner Markets, Risk Management, Volume Impact"]
    F --> O["Outcomes<br>Conditions for DEX Liquidity Viability"]