英文标题：
《Derivation of the Boltzmann Equation for Financial Brownian Motion:
Direct Observation of the Collective Motion of High-Frequency Traders》
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作者：
Kiyoshi Kanazawa, Takumi Sueshige, Hideki Takayasu, Misako Takayasu
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最新提交年份：
2018
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英文摘要：
A microscopic model is established for financial Brownian motion from the direct observation of the dynamics of high-frequency traders (HFTs) in a foreign exchange market. Furthermore, a theoretical framework parallel to molecular kinetic theory is developed for the systematic description of the financial market from microscopic dynamics of HFTs. We report first on a microscopic empirical law of traders\' trend-following behavior by tracking the trajectories of all individuals, which quantifies the collective motion of HFTs but has not been captured in conventional order-book models. We next introduce the corresponding microscopic model of HFTs and present its theoretical solution paralleling molecular kinetic theory: Boltzmann-like and Langevin-like equations are derived from the microscopic dynamics via the Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy. Our model is the first microscopic model that has been directly validated through data analysis of the microscopic dynamics, exhibiting quantitative agreements with mesoscopic and macroscopic empirical results.
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中文摘要：
通过对外汇市场高频交易者动态的直接观察，建立了金融布朗运动的微观模型。此外，还建立了一个与分子动力学理论平行的理论框架，以便从HFTs的微观动力学系统地描述金融市常我们首先通过跟踪所有个体的轨迹，报告了交易员趋势跟踪行为的微观经验法则，该法则量化了高频交易的集体运动，但在传统的订单簿模型中尚未捕捉到。接下来，我们介绍了相应的HFTs微观模型，并给出了其平行于分子动力学理论的理论解：类Boltzmann和类Langevin方程是通过Bogoliubov-Born-Green-Kirkwood-Yvon层次从微观动力学推导出来的。我们的模型是第一个通过微观动力学数据分析直接验证的微观模型，显示出与介观和宏观经验结果的定量一致性。
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分类信息：

一级分类：Quantitative Finance 数量金融学
二级分类：Trading and Market Microstructure 交易与市场微观结构
分类描述：Market microstructure, liquidity, exchange and auction design, automated trading, agent-based modeling and market-making
市场微观结构，流动性，交易和拍卖设计，自动化交易，基于代理的建模和做市
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一级分类：Physics 物理学
二级分类：Statistical Mechanics 统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
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