发表机构
School of Mathematics and Statistics, University of New South Wales; Department of Statistical Sciences, University of Cape Town（新南威尔士大学数学与统计学院; 开普敦大学统计科学系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文通过双场反应-扩散订单簿模型，在操作时间下统一解析了有限买卖价差，揭示了补单位移与穿透深度对报价响应的延迟和衰减作用。
AI 中文摘要
我们给出了一个统一的分析描述，针对双场反应-扩散订单簿中的有限买卖价差。该模型在操作时间上保留了独立的买价和卖价密度，并考虑了扩散、取消、反应和外部订单创建。在对称等系数分支上，不平衡场决定了反应价格，而总站立密度承载了价差几何。通过在一个围绕反应边界的有限区间内抑制订单放置，引入了做市商来源，代表了远离报价的往返补单位移。在分离、准静态和弱重叠近似下，运输从放置边缘向内穿透到取消长度，使得报价价差成为无放置源区间的亚阈值核心。市价单在观察到的报价处移除站立密度，而补单则在报价之外交付，必须扩散回穿透深度。我们推导了操作时间中延迟和衰减的报价级响应。在该分支上，有限价差和价格影响来自不同的响应部门，而它们在日历时间上的表现则需要一个独立的观察时钟。
英文摘要
We give a unified analytic account of a finite bid--ask spread in a two-field reaction--diffusion order book. The model retains separate bid and ask densities in operational time, with diffusion, cancellation, reaction and external order creation. On the symmetric equal-coefficient branch, the imbalance field determines the reaction price, while the total standing density carries the spread geometry. A market-making source is introduced by withholding order placement over a finite interval around the reaction boundary, representing round-trip replenishment displaced from the quote. Under a separated, quasistationary and weak-overlap approximation, transport penetrates inward from the placement edges over the cancellation length, giving the quoted spread as the sub-threshold core of the placement-source-free interval. Market orders remove standing density at the observed quote, whereas replenishment is delivered outside it and must diffuse back across the penetration depth. We derive the resulting delayed and attenuated quote-level response in operational time. On that branch, finite spread and price impact arise from distinct response sectors, while their calendar-time appearance requires a separate observation clock.
Comments6 pages, 1 figure. Reproducibility code and computational supplement: https://github.com/timgebbie/two-field-spread-reproducibility
