Motivated by recent development in structural agent models on asset pricing, explanation power and calibration issue of those models, this paper presents a simple market fraction model of two types of traders---fundamentalists and trend followers---under a market -maker scenario. It is found that asset prices, wealth dynamics and market behaviors are characterized by the dynamics of the underlying deterministic system. The model is able to explain various market behaviors, and to generate some of the stylized facts. By introducing two measures on wealth dynamics, we are able to show the limitations of profitability and rationality of different trading strategies. Six significant autocorrelation coefficient (ACs) patterns are characterized by different types of bifurcation of the underlying deterministic system. In particular, an oscillating and decaying AC pattern with positive ACs for even lags and negative for odd lags can be generated when the market is dominated by the fundamentalists (that is when the parameters are near the flip bifurcation boundary), and a positive decaying AC patterns with long memory can be generated when the market is dominated by the trend followers with high decay memory (that is when the parameters are near the Hopf bifurcation boundary). The results show a promising power of stability analysis and bifurcation theory in explaining and calibrating asset price and wealth dynamics, market behavior, and generating various econometric properties of financial data.
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