Asset Pricing Under Knight Uncertainty

Modern asset pricing theory assumes that the probability distribution of future state of financial variables are known,investors know exactly all relevant parameters,so there is no meaning to distinguish risk and Knight Uncertainty clearly.But,Knight stressed that it is important to distinguish between the two factors and,to the fact that,in the real world,Knight Uncertainty in investors' decision-making process is more universal.Ellsberg Paradox shows that people prefer to act on event which has a known probability,even if both have the same expectations and probability distribution.In addition,the classic model based on the traditional financial assumptions are constantly challenged by the financial vision just like Equity Premium Puzzle,Risk-free Rate Puzzle and so on in recent years.So we have a necessity to ponder the problem that whether investors can accurately know the probability distribution of the variable in the real world where information characterize incompletion and update rapidly.If not exactly know,then investors bear the Knight Uncertainty,and the point is that whether they should get compensation paid for undertaking it?This article assumes that under incomplete information investors bear the Knight Uncertainty.And then we study it by combing theoretical,empirical and comparative research method,deduct the theoretical model by virtue of multiple prior utility function,analysis of assets portfolio selection process under general equilibrium and the introduction of Knight uncertainty.Specifically,we assume that the process of market dividend obey two state Hidden Markov processes,such as bear and bull,and deduct again the extending ICAPM model and CCAPM model by using the method of dynamic optimization and stochastic discount factor under Risk-Knight Uncertainty-Earnings framework,and then take comparative analysis with the classical model.The models take into account the investor's learning behavior and information updating,and therefore are more realistic.Next,we use GMM estimation and ordinary least squares regression method in empirical studies,examine the applicability of the model in China's stock market and extract risk premium and Knight Uncertainty premium under incomplete information.Using the extending theoretical model to explain the financial vision and exert empirical tests,it is confirmed Knight Uncertainty is a pricing factor,investors in the investment decision-making process require to obtain Knight Uncertainty premium.The asset pricing model introducing Knight Uncertainty can be better to explain the Equity Premium Puzzle,Risk-free Rate Puzzle and Excess Volatility Puzzle in capital markets,which further supporting the fact that adding Knight Uncertainty factor into the model as a pricing factor is more powerful.In addition,by use of SSE180 index and SSE 380 index as proxy for two asset portfolios and the Shanghai Composite index as proxy for the market,analysis is put to test the extending ICAPM model and CCAPM model.The analysis to ? value showed that there exists negative correlation between the probability difference and asset return,as well as between the probability difference and consumption,and is a factor impacting capital gains rate.Equation regression analysis and it' test results support the validity of the model,that is to say,the extended model is suitable for Chinese stock market.