逃离布朗跟踪者
Escaping the Brownian stalkers
摘要：
我们提出了一个简单的模型，长期投资者在股票市场的行为，由三个粒子，这代表了当前的股票价格和意见的买方，卖方，关于正确的交易价格。随着时间的推移，两组交易者都会更新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。我们认为市场的稳定性的买家和卖家的意见之间的距离，并证明了距离过程是依赖于$γ$的经常性/瞬态。
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 $γ$, 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 $γ$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
