英文标题：
《A fractional reaction-diffusion description of supply and demand》
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作者：
Michael Benzaquen and Jean-Philippe Bouchaud
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最新提交年份：
2017
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英文摘要：
We suggest that the broad distribution of time scales in financial markets could be a crucial ingredient to reproduce realistic price dynamics in stylised Agent-Based Models. We propose a fractional reaction-diffusion model for the dynamics of latent liquidity in financial markets, where agents are very heterogeneous in terms of their characteristic frequencies. Several features of our model are amenable to an exact analytical treatment. We find in particular that the impact is a concave function of the transacted volume (aka the \"square-root impact law\"), as in the normal diffusion limit. However, the impact kernel decays as $t^{-\\beta}$ with $\\beta=1/2$ in the diffusive case, which is inconsistent with market efficiency. In the sub-diffusive case the decay exponent $\\beta$ takes any value in $[0,1/2]$, and can be tuned to match the empirical value $\\beta \\approx 1/4$. Numerical simulations confirm our theoretical results. Several extensions of the model are suggested.
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中文摘要：
我们认为，金融市场中时间尺度的广泛分布可能是在程式化的基于代理的模型中再现现实价格动态的关键因素。我们提出了一个分数反应扩散模型，用于研究金融市场中潜在流动性的动力学，其中代理在其特征频率方面非常不均匀。我们模型的几个特征可以进行精确的分析处理。我们特别发现，与正常扩散极限一样，影响是交易量的凹函数（即“平方根影响定律”）。然而，在扩散的情况下，冲击核衰减为$t ^{-\\ beta}$，而$\\ beta=1/2$，这与市场效率不一致。在次扩散情况下，衰减指数$\\β$取$[0,1/2]$中的任何值，并且可以调整以匹配经验值$\\β\\大约1/4$。数值模拟证实了我们的理论结果。提出了该模型的若干扩展。
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分类信息：

一级分类：Quantitative Finance 数量金融学
二级分类：Mathematical Finance 数学金融学
分类描述：Mathematical and analytical methods of finance, including stochastic, probabilistic and functional analysis, algebraic, geometric and other methods
金融的数学和分析方法，包括随机、概率和泛函分析、代数、几何和其他方法
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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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