Optimal Portfolio Selection Problem Based On Nonparametric Method

With the development of China's economic marketization and financial market reform,the construction of the portfolio model can not only provide an important guiding role for investors to select the optimal investment strategy,but also in the financial and economic fields,especially in the field of asset pricing and investment portfolio,portfolio investment model is also crucial.By constructing a portfolio,the investor makes reasonable allocation of assets,and according to the late feedback and market information on the construction of the portfolio to adjust,in order to ensure the superiority of their own income.Because there are many factors of stochastic uncertainty in the financial investment market,expectation utility theory in modern investment theory can solve these uncertain problems effectively.In the process of investment,the theory is that investors should be able to get the final expected utility,rather than the final wealth value.Based on the advantages of the nonparametric density estimation method,this paper constructs the portfolio model based on the different utility functions under the expected utility theory,and analyzes the optimal investment strategy of the four models by empirical research.Firstly,this paper introduces the background and significance of the research on portfolio model,and then reviews the domestic and foreign research status of the portfolio model and the nonparametric density estimation method.Then,from the perspective of portfolio model,the portfolio model based on nonparametric kernel density estimation and generalized k-nearest neighbor density estimation is established under power utility function and exponential utility function.Under the different parameters of utility function,the non parametric expression of the expected utility of four investment portfolio models is simplified.Finally,the monthly yield data of five stocks listed on China Shenzhen Stock Exchange from February 1,2016 to January 31,2017 were used as samples.Using the optimization algorithm-multiplier method,The optimal investment strategy under the different parameters of the utility function is obtained,and the comparative analysis is carried out.In this paper,we use the stock data as a sample to analyze the portfolio model based on different utility functions in the framework of nonparametric density estimation.It is found that:(1)Under the kernel density estimation framework,the parameter value of the exponential utility function will influence the optimal investment strategy of the portfolio model results.Therefore,it is possible to obtain the appropriate model by choosing the appropriate utility function and its parameter value when considering the attitude of investors and the degree of risk aversion.(2)Under the generalized k-nearest neighbor density estimation framework,different utility functions and their parameter values have little effect on the investment strategy obtained by the model.(3)Under the utility function condition,the parameter value of the utility function has little effect on the result of the portfolio model based on the same nonparametric density estimation method.(4)Under the exponential utility function,the parameter value of the utility function has a great influence on the result of the portfolio model based on the same nonparametric density estimation method.Based on the nonparametric density estimation method and the expected utility theory,this paper considers a variety of theoretical systems to improve the structure of the portfolio model.Through the comparative analysis of the optimal investment strategy of the model,it can provide investment decision suggestions for investors with different risk preferences,and improve the decision-making ability and level of asset management investment.