Paper: arXiv 2601.11375

Authors: B. K. Meister

Abstract

Three traits of decentralized finance are studied. First, the market impact function is derived for optimal-growth liquidity providers. For a standard random walk, the classic square-root impact is recovered. An extension is then derived to fit general fractional Ornstein-Uhlenbeck processes. These findings break with the linearized liquidity models used in most decentralized exchanges. Second, a Constant Product Market Maker is viewed as a multi-phase Carnot engine, where one phase matches the exchange of tokens by a liquidity taker, and another the change of pool size by a liquidity provider. Third, stablecoin de-pegging is a form of catastrophe risk. By using growth optimization, default odds are linked to the cost of catastrophe bonds. De-pegging insurance can act as a counterweight and a key marketing tool when the law forbids the payment of interest on stablecoins.

Complexity vs Empirical Score

  • Math Complexity: 6.5/10
  • Empirical Rigor: 1.5/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents interesting theoretical concepts by connecting Kelly growth optimization, fractional Ornstein-Uhlenbeck processes, and thermodynamics (Carnot engine) to DeFi market dynamics. However, it is purely mathematical/conceptual and lacks any empirical backtesting, real-world DEX data validation, or statistical testing.

Research Flowchart

  flowchart TD
    A["Research Goal: Analyze DeFi Automated Liquidity, Market Impact, Engine Analogy & De-pegging Risk"] --> B["Input Models: CPMM Mechanisms, Fractional O-U Processes & Catastrophe Risk Math"]
    
    B --> C["Derive Market Impact Functions for Optimal-Growth LPs"]
    B --> D["Model CPMM as a Multi-Phase Carnot Engine"]
    B --> E["Apply Growth Optimization & Catastrophe Bond Pricing to Stablecoins"]
    
    C --> F["Findings: Square-root impact recovered for Random Walk; challenges linear DEX models"]
    D --> G["Findings: Formalized energy-like cycle between Liquidity Takers & Providers"]
    E --> H["Findings: Linked default odds to cat-bond costs; framed de-pegging insurance as non-interest yield"]