This work concerns the modeling of evolvement of trading behavior in stock markets which can cause significant impact on the movements of prices and volatilities. Based on the assumption of the investors' limited rationality, the evolution mechanism of trading behavior is modeled according to peer effect in network, that investors are prone to imitate their neighbors' activity through comprehensive analysis on the neighboring preferred degree, self-psychological preference, and the network topology of the relationship among them. We investigate by mean-field analysis and extensive simulations the evolution of investors' trading behavior in various typical networks under different characteristics of peer effect. Our results indicate that the evolution of investors' behavior is affected by the network structure of stock market and the effect of neighboring preferred degree; the stability of equilibrium states of investors' behavior dynamics is directly related with the concavity and convexity of the peer effect function; connectivity and heterogeneity of the network play an important role in the evolution of the investment behavior in stock market.
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