英文标题：
《Mean Field Limit of a Behavioral Financial Market Model》
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作者：
Torsten Trimborn, Martin Frank, Stephan Martin
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最新提交年份：
2017
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英文摘要：
In the past decade there has been a growing interest in agent-based econophysical financial market models. The goal of these models is to gain further insights into stylized facts of financial data. We derive the mean field limit of the econophysical model by Cross, Grinfeld, Lamba and Seaman (Physica A, 354) and show that the kinetic limit is a good approximation of the original model. Our kinetic model is able to replicate some of the most prominent stylized facts, namely fat-tails of asset returns, uncorrelated stock price returns and volatility clustering. Interestingly, psychological misperceptions of investors can be accounted to be the origin of the appearance of stylized facts. The mesoscopic model allows us to study the model analytically. We derive steady state solutions and entropy bounds of the deterministic skeleton. These first analytical results already guide us to explanations for the complex dynamics of the model.
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中文摘要：
在过去十年中，人们对基于代理的经济物理金融市场模型越来越感兴趣。这些模型的目标是进一步深入了解金融数据的程式化事实。我们由Cross、Grinfeld、Lamba和Seaman（Physica A，354）推导了经济物理模型的平均场极限，并表明动力学极限是原始模型的良好近似。我们的动力学模型能够复制一些最突出的程式化事实，即资产回报的厚尾、不相关的股票价格回报和波动性聚类。有趣的是，投资者的心理误解可以解释为程式化事实出现的根源。介观模型允许我们对模型进行分析研究。我们推导了确定性骨架的稳态解和熵界。这些最初的分析结果已经为我们解释模型的复杂动力学提供了指导。
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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：Mathematics 数学
二级分类：Analysis of PDEs 偏微分方程分析
分类描述：Existence and uniqueness, boundary conditions, linear and non-linear operators, stability, soliton theory, integrable PDE\'s, conservation laws, qualitative dynamics
存在唯一性，边界条件，线性和非线性算子，稳定性，孤子理论，可积偏微分方程，守恒律，定性动力学
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