Partially Active Automated Market Makers

Paper: arXiv 2602.09887

Authors: Sunghun Ko

Abstract

We introduce a new class of automated market maker (AMM), the \emph{partially active automated market maker} (PA-AMM). PA-AMM divides its reserves into two parts, the active and the passive parts, and uses only the active part for trading. At the top of every block, such a division is done again to keep the active reserves always being (λ)-portion of total reserves, where (λ\in (0, 1]) is an activeness parameter. We show that this simple mechanism reduces adverse selection costs, measured by loss-versus-rebalancing (LVR), and thereby improves the wealth of liquidity providers (LPs) relative to plain constant-function market makers (CFMMs). As a trade-off, the asset weights within a PA-AMM pool may deviate from their target weights implied by its invariant curve. Motivated by the optimal index-tracking problem literature, we also propose and solve an optimization problem that balances such deviation and the reduction of LVR.

Complexity vs Empirical Score

• Math Complexity: 6.5/10
• Empirical Rigor: 3.0/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents a novel framework for mitigating Loss-Versus-Rebalancing (LVR) in AMMs by framing LP rebalancing through an optimal execution lens with partially active reserves. The theoretical formulation and proofs are rigorous, clear, and mathematically sound, though it currently lacks extensive empirical backtesting or real-world transaction data validation.

Research Flowchart

  flowchart TD
    A["Research Goal: Mitigate LP Adverse Selection Costs (LVR) in CFMMs"] --> B["Propose PA-AMM Mechanism"]
    
    subgraph Methodology & Processing
        B --> C["Divide Reserves at Block Start: Active (λ) vs Passive (1-λ)"]
        D["Inputs: Block Asset Prices & Activeness Parameter λ ∈ (0, 1]"] --> C
        C --> E["Formulate Optimization Problem: Balance LVR Reduction vs Weight Deviation"]
    end

    E --> F["Outcome 1: Reduced LVR & Improved LP Wealth"]
    E --> G["Outcome 2: Solved Optimal Reserve Allocation Strategy"]

Cited References (39)

1. Measuring cex-dex extracted value and searcher profitability: The darkest of the mev dark forest — → 2507.13023
2. Automated market making and loss-versus-rebalancing (2022) — link
3. Predictable losses of liquidity provision in constant function markets and concentrated liquidity markets (2023)
4. Augmenting batch exchanges with constant function market makers (2024)
5. Arbitrageurs’ profits, LVR, and sandwich attacks: batch trading as an AMM design response (2023) — link
6. Designing a Dynamic Fee Policy that Outperforms All Uniswap ETH/USDC Pools (2022)
7. Strategic Bonding Curves in Automated Market Makers (2024) — link
8. Automatic market-making with dynamic peg (2021)

9 of 39 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.