This chapter first surveys empirical patterns that appear in asset returns. Some of the main patterns are the following. Returns are hard to predict out of sample. The correlation dimension is rather large and is unstable; i.e., returns are generated by a "complex" process, Detrended volume of trading activity is persistent, i.e., the autocorrelation function is positive and decreases slowly as lag length increases. Volatility of returns is also persistent and the autocorrelation function of volatility is rather similar to that of detrended volume. Detrended volume and volatility are highly correlated contemporaneously. The chapter sketches development of adaptive evolutionary theoretic financial asset pricing models that nest the usual rational expectations type of models. It reviews some studies of the types of structures of belief heterogeneity that is needed to generate equilibrium returns, volume of trading, and volatility of returns that is consistent with the stylized facts reviewed.
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