A Capital Asset Pricing Model With Learning Strength And Empirical Analysis

The risk attitudes for two kinds of investors vary over time due to psychological factors such as prospect theory,which refers to the reversing of risk aversion/risk loving in the case of gains/losses.So based on prospect theory,this paper introduce a time varying risk aversion for fundamentalists.If the deviation of the risk asset price from the fundamental price become more lager and lager,the risk aversion coefficient for fundamentalists will become smaller and smaller and then introduce a stable factor.For the chartists by considering a nonlinear function impacted by learning strength.Using the theory of difference equation,we analyze the equilibrium solution?stability and bifurcation of model.Finally,we get the following conclusion:learning strength can damage to market and stable factor can stable market.Finally,we generalize the abstract function and through the numerical simulation,we compare the return series of this model,the Beum-Jo Park(2014)model and the shangzheng index and verify the new model is better than before in describing the non-normality and the volatility clustering of the return series and the correlation of the square return series.