Table of Contents

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  • Section: Introduction
    • Introduction
  • Section: AMM Models
  • Section: AMM Mathematics
    • General AMM Mathematics
      • Key concepts
      • The micro economics of the price response function
        • Demand and supply curves in microeconomics
        • Supply and demand curves in financial markets
        • Supply and demand curves in market making
        • Aggregating PRFs
        • Optimal routing
      • AMM characteristic functions
        • Scaling symmetry
        • Transformations
        • Conditions characteristic functions must satisfy
      • The mathematics of multi-asset pools
        • Definitions
        • Consistency and geometry
    • AMMs and financial derivatives
      • Black Scholes and derivatives pricing
      • Calls, puts and European profile matching
        • The strike density function and the Cash Gamma
      • Power law profiles under Black Scholes
      • Analysing the constant product AMM as a financial derivative
    • Mathematics of specific AMMs
      • Constant product (k=x*y)
      • Constant sum (k=x+y)
      • Concentrated, range-bound and levered liquidity
        • Range-bound liquidity
        • Concentrated and levered liquidity
        • Divergence loss with concentrated liquidity
      • Modified weights
      • Modified curve aka (2 token) stableswap
        • Dynamic Chi
      • Time varying curve
      • [Mooniswap]
      • Multi asset
        • Equal weights
        • Variable weights
  • Section: AMM Economics
  • Section: AMM Regulations
  • Section: AMM Eco System
  • Section: Conclusion
  • Section: References
    • Glossary
      • General Glossary
      • Mathematical Glossary
    • Protocols
    • Formulas