摘要翻译：
我们提出了一个简单的股票市场长期投资者行为模型，由三个粒子组成，这三个粒子分别代表股票的当前价格和买卖双方对正确交易价格的看法。随着时间的推移，两组交易者都更新了他们对当前价格的看法。更新速度由参数$\γ$控制，价格过程由几何布朗运动描述。我们用买卖双方意见之间的距离来考虑市场的稳定性，证明了这种距离过程是依赖于$\γ$的反复/瞬态过程。
---
英文标题：
《Escaping the Brownian stalkers》
---
作者：
Alexander Weiss
---
最新提交年份：
2008
---
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
--
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
--
一级分类：Quantitative Finance        数量金融学
二级分类：Pricing of Securities        证券定价
分类描述：Valuation and hedging of financial securities, their derivatives, and structured products
金融证券及其衍生产品和结构化产品的估值和套期保值
--

---
英文摘要：
  We propose a simple model for the behaviour of longterm investors on a stock market, consisting of three particles, which represent the current price of the stock and the opinion of the buyers, respectively sellers, about the right trading price. As time evolves, both groups of traders update their opinions with respect to the current price. The update speed is controled by a parameter $\gamma$, the price process is described by a geometric Brownian motion. We consider the stability of the market in terms of the distance between the buyers' and sellers' opinion, and prove that the distance process is recurrent/transient in dependence on $\gamma$.
---
PDF链接：
https://arxiv.org/pdf/0803.3590