Automated Market Makers face a geometric dilemma: expanding liquidity depth to reduce execution slippage increases Liquidity Providers' exposure to toxic arbitrage, quantified as Loss-Versus-Rebalancing (LVR). We study the Hybrid Liquidity-Collateral Pool (HLCP), a stylized architecture that aims to partially decouple execution quality from active risk exposure through an N-scaled virtual invariant and a collateral buffer. The analysis first characterizes the geometric divergence between execution slippage and marginal-price deviation, then uses this divergence to motivate a trigger-based collateral injection rule. In a stylized duopoly model, under hyper-saturated background liquidity and non-zero volatility or collateral yield, adopting the HLCP is a Nash equilibrium and Pareto-improving relative to a standard AMM benchmark. Empirically, we examine two settings. Under a stochastic-volatility-with-jumps stress scenario, the trigger policy avoids one-shot total buffer depletion under the imposed control law and simulated shock path. Using 2025 Uniswap V2 data with zero collateral yield, the HLCP exhibits lower realized LVR and higher net LP return than the standard CPMM benchmark in the sample considered.

翻译：自动做市商面临一个几何困境：扩大流动性深度以减少执行滑点，会增加流动性提供者暴露于有毒套利的风险（以损失-再平衡差（LVR）量化）。本文研究了混合流动性-抵押池（HLCP）——一种旨在通过N尺度虚拟不变式和抵押缓冲器部分解耦执行质量与主动风险暴露的典型架构。分析首先刻画了执行滑点与边际价格偏差之间的几何散度，进而利用该散度提出基于触发机制的抵押注入规则。在一个简化双头模型下，当背景流动性过饱和且存在非零波动性或抵押收益时，采用HLCP构成纳什均衡，且相对于标准AMM基准实现了帕累托改进。实证方面，我们考察了两个场景。在带有跳跃的随机波动率压力情景下，所提出的触发策略在给定控制律与模拟冲击路径下避免了单次完全耗竭缓冲池。使用2025年Uniswap V2数据（零抵押收益），HLCP在样本中展现出比标准CPMM基准更低的实际LVR和更高的LP净收益。