Paper: arXiv 2405.18728

Abstract

Automated market makers with concentrated liquidity capabilities are programmable at the tick level. The maximization of earned fees, plus depreciated reserves, is a convex optimization problem whose vector solution gives the best provision of liquidity at each tick under a given set of parameter estimates for swap volume and price volatility. Surprisingly, early results show that concentrating liquidity around the current price is usually not the best strategy.

Complexity vs Empirical Score

  • Math Complexity: 7.5/10
  • Empirical Rigor: 2.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper employs advanced convex optimization and water-filling algorithms, but lacks backtest results, statistical metrics, or production-ready implementation details, focusing instead on theoretical problem formulation.

Research Flowchart

  flowchart TD
  A["Research Goal: Maximize fees & reserves<br>in CLMM liquidity provision"] --> B["Model as<br>Convex Optimization Problem"]
  B --> C["Inputs: Swap Volume &<br>Price Volatility Estimates"]
  C --> D["Compute: Optimal Tick-by-Tick<br>Liquidity Distribution"]
  D --> E["Outcome 1: Liquidity is<br>not best concentrated at current price"]
  D --> F["Outcome 2: Programmable tick-level<br>solution for fee maximization"]

Cited References (8)

  1. CVXPY : A P ython-embedded modeling language for convex optimization (2016)
  2. Convex Optimization (2004)
  3. Constant Function Market Makers: Multi-Asset Trades via Convex Optimization (2021) — link
  4. Panoptic: the perpetual, oracle-free options protocol (2023) — link
  5. Automated Market Making and Loss-Versus-Rebalancing (2023) — link
  6. Improved Price Oracles: Constant Function Market Makers (2020) — link
  7. Replicating Market Makers (2021) — link
  8. The pricing of options and corporate liabilities (1973)

0 of 8 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.