AI 中文总结
本研究将平方根价格冲击定律融入LMF模型构建严格可解非线性时间序列模型，解决了长程相关市价单流下的扩散价格动力学悖论，证明该模型下价格动力学长时仍具扩散性，凸显了平方根定律对理解有效市场假说微观基础的重要性。
AI 中文摘要
我们将平方根价格冲击定律融入Lillo-Mike-Farmer（LMF）模型，构建了一个严格可解的非线性时间序列模型，以解决可预测市价单流下的扩散价格动力学悖论。在金融市场微观结构中，长期以来公认价格动力学在长时尺度下近似由布朗运动描述。但同样为人熟知的是，市价单流因长程相关性而具有明确的可预测性，这一点已由LMF模型从数学上予以表述。由于市价单通常具有正价格冲击，可预测的市价单流似乎与布朗价格动力学相矛盾。本研究通过构建基于平方根价格冲击定律、推广LMF模型的非线性时间序列模型，解决了这一扩散价格动力学悖论。我们的时间序列模型可在数学上映射到统计物理学中一类严格可解的非马尔可夫随机过程——莱维行走（Lévy-walk）框架。我们证明，即使在可预测市价单流下，基于平方根定律的价格动力学在长时尺度下仍具有扩散性。本研究凸显了平方根定律在理解有效市场假说的微观结构基础方面的关键实践意义。
英文摘要
We develop an exactly solvable nonlinear time-series model by incorporating the square-root price-impact law into the Lillo--Mike--Farmer (LMF) model to resolve the diffusive price-dynamics paradox under predictable market-order flow. In financial market microstructure, it is well established that the price dynamics are approximately described by Brownian motion at long times. However, it is also well-known that market-order flow is clearly predictable due to long-range correlations, as mathematically formulated by the LMF model. Since market orders have a positive price impact in general, predictable market-order flow seems to contradict Brownian price dynamics. In this work, we resolve this diffusive price-dynamics paradox by developing nonlinear time-series models that generalize the LMF model based on the square-root price-impact law. Our time-series models can be mathematically mapped onto the Lévy-walk framework---an exactly solvable class of non-Markovian stochastic processes developed in statistical physics. We prove that the price dynamics are diffusive at long times under the square-root law even under predictable market-order flow. Our work highlights the crucial practical importance of the square-root law in understanding the microstructural foundation of the Efficient Market Hypothesis.
Comments25 pages, 15 figures
