# Escaping the Brownian stalkers - Quantitative Finance > Trading and Market Microstructure

Abstract: We propose a simple model for the behaviour of longterm investors on a stockmarket, consisting of three particles, which represent the current price of thestock and the opinion of the buyers, respectively sellers, about the righttrading price. As time evolves, both groups of traders update their opinionswith respect to the current price. The update speed is controled by a parameter$\gamma$, the price process is described by a geometric Brownian motion. Weconsider the stability of the market in terms of the distance between thebuyers- and sellers- opinion, and prove that the distance process isrecurrent-transient in dependence on $\gamma$.

Author: Alexander Weiss

Source: https://arxiv.org/