Empirical Study Of Portfolio Selection Model With Random Fuzzy Variable Returns And Weighted Max-Min Operator

Securities market is a complex and dynamic system, and the process of economic globalization and financial integration accelerates the complexity and volatility of securities market. Regarding the security return as a random fuzzy variable can both reflect the randomness and fuzziness of the stock market. In addition, the paper uses the modern behavioral research achievements to take investors’ real psychological preferences into consideration, and build portfolio model with weighted max-min operator. In order to solve the model with transaction cost and minimize trading unit, the paper improves the dynamic neighbor particle swarm optimization and proposes improved dynamic neighbor particle swarm optimization. To test the validity of the model, this paper use the improved dynamic neighbor swarm optimization to solve the weighted max-min random fuzzy portfolio problem based on the domestic economic situation. The paper includes the following several aspects:(1) Considering the uncertainty of both randomness and fuzziness in the securities market, this paper takes the security return as a random fuzzy variable and constructs expected portfolio return membership function based on wealth variation. Moreover, this membership function can reflect both the expected return and target probability of investors by using weighted max-min operator to build the weighted max-min random fuzzy portfolio. To study the efficient frontier of this model, we use historical data and the mean-variance portfolio model of Markowitz to make a comparison. The results show that the efficient frontier of the portfolio with weighted max-min operator and random fuzzy variable is inconsistent with that of the Markowitz’s mean-variance portfolio model.(2) According to the shortcomings of the dynamic neighbor particle swarm optimization algorithm, this paper proposes improved dynamic neighbor particle swarm optimization algorithm by improving the method of the particle initialization and the topological structure of the dynamic neighbor. This paper tests the portfolio without weighted constraints and with weighted constraints respectively and finds that the improved dynamic neighbor particle swarm algorithm can effectively solve the problems of the efficient frontier of the portfolio.(3) Selecting50stocks from Hushen300index randomly, we make an empirical test on the portfolio with weighted max-min operator and random fuzzy variable. The empirical study is divided into two parts.①In a friction-free market, comparing the investment performance of weighted max-min random fuzzy portfolio, Markowitz mean-variance portfolio and Vercher fuzzy portfolio. The results show that the model proposed by this paper is superior to the Markowitz mean-variance model and the Vercher fuzzy model.②In a market with friction, setting different portfolio parameters for investors with different risk attitudes. The model results which are solved by improved dynamic neighbor particle swarm optimization algorithm show that this portfolio model can effectively reflect the psychological preferences of investors with different risk attitudes.