The Research On The Portfolio Programming In The Fuzzy Environment

The core question of the portfolio’s decision-making research is to study how to distribute the limiting funds to the different assets in order to achieve the goal which to spread the loss and to ensure the earnings. And in essence, based on the research of the modern portfolio theory, the portfolio investment programming is the research method in the uncertainty environment which to establish the mathematic programming model which can simulate the actual investment complexions, and on the condition of the synthetical balance of the correlative factors, such as, the investment return and the investment risk, to construct the analytic framework of the investment decision, then solve the optimal investment decision. Using the correlative theories of the probability to measure the uncertainty of the security market, and under the basal analytic framework of the modern portfolio theary, Markowitz’s mean-variance model is the security programming model which minimize the investment risk on the condition of the certain investment return, or maximize the invesetment retun on the condition of the certain investment risk.However, there are two uncertainty events in the security market: the stochastic uncertainty events and the fuzzy uncertainty events, then the security investment programming can correspondingly be classified the security investment programming model measuring the stochastic uncertainty events and the security investment programming model measuring the fuzzy uncertainty events. Based on the probability theory, mean-variance model only considers the stochastic uncertainty of the security market, while ignores the impact of the fuzzy uncertainty. The uncertainty of the security market is showed more fuzzy uncertainty. The fuzzy uncertainty is the intrinsic and essence characteristic of the security market, establishing the security portfolio programming under the fuzzy uncertainty environment will be more suitable the actual investment decision. Based on the actual situation of our country, by making fully use of the approach which to combine the quantitative and qualitative knowledge, and using the knowledge and experience of the expert, and on the basis of the in-depth digging the fuzzy characteristics of the security market, this study is to research the selectable question of the security investment portfolio by synthetically using the fuzzy theory and optimal method in order to give the effective decision-making advice for the investment practice of our country. The main concern of this study is following aspects:(1) The constructing and applied research of the portfolio in the fuzzy environment. Under the fuzzy uncertainty environment, I have constructed the portfolio programming, and gived the optimal and solving methods correspondingly, then studied the decision-making impact of the fuzzy portfolio programming in the investment decision-making practice, and then based on the construction and the optimal solution of the single-period portfolio programming, I have studied the investment decision-making impact of the multi-period fuzzy portfolio programming for the choices of the securities.(2) The portfolio validity research in the fuzzy environment. The future return states of the portfolio forecasted by the fuzzy AR model is taken the place of the sample expectation to measure the investment return, and under the framework of the fuzzy decision-making theory, the investment risk measured by the absolute deviation is adjusted by the fuzzy relaxation constraint, and I construct a fuzzy investment programming which the goal function is the investment return of the trapezoidal fuzzy number and the risk constraint is the fuzzy relaxation constraint, compare and analyze the effective frontier of the fuzzy environment and the stochastic environment, and study the validity of the investment programming under the fuzzy environment and the superiority of the compare between the fuzzy portfolio programming and the stochastic portfolio programming.(3) The investment programming research of the two-goal trapezoid fuzzy number under the fuzzy environment. I establish the predicting model which the security price is the trapezoidal fuzzy numbers based on the prediction of the fuzzy time series, and measuring the investment return by the ratio of the predicting value and measuring the purchasing price and the investment risk by the semi-absolute deviation which the predicting value is below to the expectation, I construct the two-goal programming, and solve the programming to obtain the optimal solution with the method of the compromise programming based on simulating the trapezoid fuzzy number of the security price by fully using the open price, the close price, the highest price and the lowest price of the security market, then empirically analyze the perform of the fuzzy model with the actual data of the SSE50, and then compare the portfolio perform with the mean-absolute deviation model under the probability framework.(4) The portfolio decision-making research of the two-goal interval number under the fuzzy environment. I use the S-type membership to describe the satisfaction degree level of the investment return, and make use of the fuzzy logic relationship to forecast the future satisfaction degree level, then establish the two-goal interval number investment programming which the fuzzy goal is the interval return and the interval risk, and then empirically analyze this fuzzy programming with the actual data of the SSE180.(5) The multi-period portfolio optimization research under the fuzzy environment. I spread the fuzzy single programming into the multi-period portfolio, and use the fuzzy AR model that the fuzzy variables are the triangular fuzzy number to predict the future multi-period investment returns, then measure the investment risk with the variance and covariance of the triangular fuzzy number, and then construct the multi-period portfolio model, and solve the optimal solution by using the PSO algorithm with the factor of the genetic cross and the genetic variation, at last, empirically analyze this programming with the actual data of the Shenzhen Security Market.(6) The multi-period decision-making research based on the two-step fuzzy chance programming. I predict the investment return by using the fuzzy AR model which the fuzzy variables are the symmetric triangular fuzzy number, and measure the investment risk by the covariance of the fuzzy return middle-value, then introduce the market liquidity into the investment decision-making framework, and then change the predictive fuzzy return to the clear investment return by using the clear formula of the fuzzy number, and based on the establishment the single two-step fuzzy chance programming, I establish a two-stage chance programming in order to obtain the Pareto solution of the investment return and the investment risk, then use the PSO algorithm with the factor of the genetic cross and the genetic variation to solve the optimal solution under the framework of the dynamic programming, and then empirically analyze this programming with the actual data of the SSE.50.(7) The multi-period fuzzy AHP asset allocation research based on the scenarios tree under the fuzzy environment. Using the fuzzy AHP method, I introduce the fundamental factors of the financial asset into the framework of the investment analysis, and use the absolute deviation and the relative deviation between the factor variables, then construct the fuzzy judgment matrix, then based on the synthetic evaluate value of the triangular fuzzy return and the synthetic evaluate value of the triangular fuzzy risk, establish the single asset allocation under fuzzy environment, and then with the multi-period framework of the scenarios tree model and the probability appeared the fuzzy logic relationship between the market states, calculate the corresponding Bayesian probability, then extend the single fuzzy investment programming into the multi-period fuzzy asset allocation model, and then empirically analyze the programming with the actual data of the SHSZ300Industry Index.Finally, the main contents and results of our research in this dissertation are summarized as well as future research directions.