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：扩大流动性深度以降低执行滑点，会增加流动性提供者对有害套利（即再平衡损失，LVR）的暴露。本文研究混合流动性-抵押池（HLCP），这是一种通过N阶虚拟不变量和抵押缓冲池，旨在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，进而利用该散度推导基于触发机制的抵押注入规则。在典型双寡头模型中，当背景流动性处于超饱和状态且存在非零波动率或抵押品收益时，采用HLCP构成纳什均衡，并相对于标准AMM基准实现帕累托改进。实证部分检验了两种场景：在随机波动率带跳的应力场景下，触发策略在施加的控制律与模拟冲击路径下避免了单次完全耗尽缓冲池；基于2025年Uniswap V2数据（零抵押品收益），在样本期内HLCP的实际LVR低于标准恒定乘积做市商（CPMM）基准，且净LP收益更高。