AI 中文总结
本文为信息中性交易策略产生扩散型冲击状态的结论构建微观基础，推导了冲击定律形式，分析了冲击阶段的经济意义及衰减特性。
AI 中文摘要
结构性价格扩散性解释了市场冲击的诸多经验规律，包括“平方根定律”及其在低交易率下向线性制度的转变[1]。其核心预测之一是，信息中性的交易策略会产生扩散型冲击状态。我们在包含一名交易者和众多套利者的经济体中为这一结果构建微观基础，这些套利者会逐步消除可预测的收益。每个套利者观测已实现收益和基本面收益某一成分的私人信号。当总私人信息变得完整且在适当收敛至平稳极限时，交易者的冲击定律形式为 $j=U\cdot w$，其中 $w$ 是交易计划的创新，$U$ 是因果全通滤波器。因此，冲击收益是白噪声，即使没有单个套利者能重构潜在的交易策略。随后我们研究冲击阶段的经济意义，我们认为，与生成交易流的滤波器 $L$ 距离最小的 $U$ 是特别有趣的候选：此时交易流在冲击和套利下被最小程度扭曲，且始终保证正的冲击成本。在由双指数 $L$（我们模型中允许的最简单形式）生成的交易流下，出现一个有趣的结果：冲击衰减被限制在50%–60%的窄区间内，低于一些经验估计值，且与其他估计值相当一致。更复杂的流模型可导致不同的衰减。最后，我们认为在真实市场中，冲击阶段的长期尾部可能略有“扭曲”，这允许冲击传播子完全松弛，该效应是冲击状态的弱长期均值回归。
英文摘要
Structural price diffusivity explains many empirical regularities of market impact including the ``square-root law'' and its crossover to a linear regime for low trading rates \citep{bonart2026diffusive}. One of its central predictions is that an information-neutral trading strategy generates a diffusive impact state. We microfound this result in an economy with a trader and many arbitrageurs who progressively eliminate predictable returns. Each arbitrageur observes realized returns and a private signal of one component of the fundamental return. As aggregate private information becomes complete and under suitable convergence to a stationary limit, the trader's impact law is of the form $j=U\cdot w$, where $w$ is the innovation in the trading schedule and $U$ is causal all-pass. Impact returns are therefore white, even though no individual arbitrageur can reconstruct the underlying trading strategy. We then investigate the economic meaning of the impact phase. We argue that the $U$ which has minimum distance from the filter $L$ generating the trade flow is an especially interesting candidate: Trade flow is then minimally distorted under impact and arbitrage, and it always guarantees positive impact costs. Under a trader flow generated by a biexponential $L$ (the simplest form allowed in our model) an interesting result emerges: Impact decline is confined to a narrow band of $50\%$--$60\%$, lower than some empirical estimates and quite consistent with others. More complicated flow models can lead to different decays. Finally, we argue that in real markets, the impact phase is probably somewhat ``distorted'' in its long-term tails which allows for a full relaxation of the impact propagator. The effect is weak, long-term mean-reversion of the impact state.
