摘要翻译：
我们引入并严格地处理了一个新的连续双重拍卖的多Agent模型，也就是订货簿模型。它旨在解释当影响市场的新信息到达时市场的集体行为。该模型的新特点是增加了两个缓慢变化的参数，即所谓的情感函数。这些情绪函数衡量了两类投资者的公平价格概念，即多头和空头。我们的模型给出了情绪函数时间演化的微分方程，并构成了一个具有长期相关性的非线性马尔可夫过程。我们解释了情绪函数方程背后的直觉，并给出了数值模拟，表明我们的模型的行为类似于真实市场的行为。我们还得到了变波动率的Ornstein-Uhlenbeck型过程模型的一个扩散极限。波动性与多头和空头对证券公平价格的意见分歧成正比。本文是对我们以前工作的补充，并给出了数学证明。
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英文标题：
《Investor's sentiment in multi-agent model of the continuous double
  auction》
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作者：
A. Lykov, S. Muzychka, K. Vaninsky
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最新提交年份：
2016
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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：Mathematical Physics        数学物理
分类描述：Articles in this category focus on areas of research that illustrate the application of mathematics to problems in physics, develop mathematical methods for such applications, or provide mathematically rigorous formulations of existing physical theories. Submissions to math-ph should be of interest to both physically oriented mathematicians and mathematically oriented physicists; submissions which are primarily of interest to theoretical physicists or to mathematicians should probably be directed to the respective physics/math categories
这一类别的文章集中在说明数学在物理问题中的应用的研究领域，为这类应用开发数学方法，或提供现有物理理论的数学严格公式。提交的数学-PH应该对物理方向的数学家和数学方向的物理学家都感兴趣；主要对理论物理学家或数学家感兴趣的投稿可能应该指向各自的物理/数学类别
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一级分类：Mathematics        数学
二级分类：Mathematical Physics        数学物理
分类描述：math.MP is an alias for math-ph. Articles in this category focus on areas of research that illustrate the application of mathematics to problems in physics, develop mathematical methods for such applications, or provide mathematically rigorous formulations of existing physical theories. Submissions to math-ph should be of interest to both physically oriented mathematicians and mathematically oriented physicists; submissions which are primarily of interest to theoretical physicists or to mathematicians should probably be directed to the respective physics/math categories
math.mp是math-ph的别名。这一类别的文章集中在说明数学在物理问题中的应用的研究领域，为这类应用开发数学方法，或提供现有物理理论的数学严格公式。提交的数学-PH应该对物理方向的数学家和数学方向的物理学家都感兴趣；主要对理论物理学家或数学家感兴趣的投稿可能应该指向各自的物理/数学类别
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一级分类：Mathematics        数学
二级分类：Probability        概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
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英文摘要：
  We introduce and treat rigorously a new multi-agent model of the continuous double auction or in other words the order book (OB). It is designed to explain collective behaviour of the market when new information affecting the market arrives. The novel feature of the model is two additional slow changing parameters, the so-called sentiment functions. These sentiment functions measure the conception of the fair price of two groups of investors, namely, bulls and bears. Our model specifies differential equations for the time evolution of sentiment functions and constitutes a nonlinear Markov process which exhibits long term correlations. We explain the intuition behind equations for sentiment functions and present numerical simulations which show that the behaviour of our model is similar to the behaviour of the real market. We also obtain a diffusion limit of the model, the Ornstein-Uhlenbeck type process with variable volatility. The volatility is proportional to the difference of opinions of bulls and bears about the fair price of a security. The paper is complimentary to our previous work where mathematical proofs are presented.
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PDF链接：
https://arxiv.org/pdf/1208.3083