Dynamics Evolution of Trading Strategies of Investors in Financial Market

This paper analyzes investors' trading strategies based on the theory of evolutionarily stable strategies and replicator dynamics model. Under the assumptions closer to a real market, we reveal the relationships between the investor's price anticipation and equilibrium sustained state. If the mean value of price deviation anticipated by investors is a negative value, there is one equilibrium sustained solution. And if the mean value of price deviation anticipated by investors is a positive value, one equilibrium sustained solution or two equilibrium sustained solutions are likely to appear in our models. This research is beneficial to evaluate differences in revenues between rational traders and noise traders, to understand dynamic evolutionary process of trading strategies, and to find equilibrium sustained solution. In addition, financial crisis as an exogenous factor is introduced into the evolutionary model. Based on theoretical analysis and simulation experiment, the results show that case 3 in theoretical analysis does not occur in the simulation after the outbreak of financial crisis, and case 1 and case 2 in theoretical analysis correspond to the different regions of the anticipated price deviation curves. Moreover, the changes of two equilibrium sustained solutions show opposite tendency characteristics with an increasing of the mean value of price deviation of risk asset. Relative to the existing research results, this paper distinguishes the different yield between risk assets and riskless assets, and considers the existence of transaction cost, assumes investors having different risk aversion coefficient, and takes financial crisis as an example to research the impacts of exogenous variables on investors' trading strategies. Through comparative analysis, the conclusions drawn from simulation experiment are consistent with equilibrium sustained solutions in theoretical analysis.