Liquidity providers (LPs) are essential figures in the operation of automated market makers (AMMs); in exchange for transaction fees, LPs lend the liquidity that allows AMMs to operate. While many prior works have studied the incentive structures of LPs in general, we currently lack a principled understanding of a special class of LPs known as Just-In-Time (JIT) LPs. These are strategic agents who momentarily supply liquidity for a single swap, in an attempt to extract disproportionately high fees relative to the remaining passive LPs. This paper provides the first formal, transaction-level model of JIT liquidity provision for a widespread class of AMMs known as Concentrated Liquidity Market Makers (CLMMs), as seen in Uniswap V3, for instance. We characterize the landscape of price impact and fee allocation in these systems, formulate and analyze a non-linear optimization problem faced by JIT LPs, and prove the existence of an optimal strategy. By fitting our optimal solution for JIT LPs to real-world CLMMs, we observe that in liquidity pools (particularly those with risky assets), there is a significant gap between observed and optimal JIT behavior. Existing JIT LPs often fail to account for price impact; doing so, we estimate they could increase earnings by up to 69% on average over small time windows. We also show that JIT liquidity, when deployed strategically, can improve market efficiency by reducing slippage for traders, albeit at the cost of eroding average passive LP profits by up to 44% per trade.

翻译：流动性提供者是自动做市商运行中的关键角色；通过提供流动性，他们换取交易费用，使自动做市商得以运作。尽管已有大量研究探讨了流动性提供者的一般激励结构，但目前我们对一类特殊的流动性提供者——即时流动性提供者——缺乏基于原理的理解。这些策略性主体为单次交换瞬时提供流动性，试图相对于其他被动流动性提供者获取不成比例的高额费用。本文针对一类广泛使用的自动做市商——集中流动性做市商（例如Uniswap V3中的实现），首次提出了交易层面的即时流动性供给形式化模型。我们刻画了这些系统中的价格冲击和费用分配格局，构建并分析了即时流动性提供者面临的非线性优化问题，并证明了最优策略的存在性。通过将即时流动性提供者的最优解应用于实际集中流动性做市商，我们观察到在流动性池中（尤其是涉及风险资产的池子），实际观测到的即时流动性行为与最优行为之间存在显著差距。现有即时流动性提供者往往未考虑价格冲击；若考虑此因素，我们估计在短时间窗口内其收益平均可增加高达69%。我们还表明，策略性部署即时流动性能够通过降低交易者的滑点来提高市场效率，尽管代价是每笔交易平均侵蚀被动流动性提供者高达44%的利润。