基于随机动力系统的证券市场演化动态研究

为刻画异质交易者并存证券市场的演化动态,分析非理性交易者在市场中是否会最终灭绝,建立了一个随机动力系统模型,将新进入者对市场演化长期均衡的影响纳入模型,描述作为开放系统的证券市场演化轨迹。通过对模型的分析,讨论了模型解的存在性和唯一性,分析了市场演化系统的长期发展动态,证明在一定条件下,非理性交易者也可以在市场中长期存在。

Stock Market Evolution Research Based on Random Dynamic System

Alchian, Friedman and Fama proposed that market participants who pursued the maximum return would survive and profit, and irrational traders would be ultimately eliminated due to long term losses. It was called Market Selection Hypothesis. The law of securities market evolution is analyzed in this paper where rational traders and irrational traders coexist by ideas of biological evolution. A differential dynamic system model, as well as a random dynamic system model, is established to describe a law of stock market evolution. It is discussed whether irrational traders should be eliminated by securities market evolution. The impact of new entrants on securities market evolutionary long-term equilibrium is considered. As well, the existence and uniqueness of the model's solution are discussed. Based on the model, using Ito's lemma, it is proved irrational traders could exit in the long-term under some conditions. Finally the suggested conclusion is verified through numerical simulation.