Abstract: 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.

Key words: behavior finance, irrational traders, stock market evolution, random dynamical system