Research On Multi-period Possibilistic Portfolio Model Under Uncertain Exit Time

Since Markowitz put forward the classical portfolio theory,scholars have studied the portfolio under stochastic environment comprehensively and achieved some results under fuzzy environment as well.Multi-period investment is common in reality,so scholars have studied lots of relevant results in both random and fuzzy environment.In recent years,uncertain exit time,which has a significant impact on profit,has attracted more and more attention by scholars.But most of their studies are under random environment.Therefore,this dissertation studies the multi-period portfolio selection problem with uncertain exit time under the fuzzy environment,which is based on the possibility theory and the upper and lower possibility theory.The dissertation's main contents are as follows:(1)Based on the possibility theory,a multi-period portfolio model with given exit time and transaction costs is studied.Assuming assets' return is a fuzzy number,and trapezoidal fuzzy number is used in our empirical research.In order to simulate real investment,we consider transaction costs in the multi-period model.Then we construct single-period portfolio models,and multi-period possibilistic portfolio models with and without transaction costs.Finally,we use real market data as an example to verify the feasibility and rationality of the model,and illustrate that transaction costs are indispensable in the multi-period model.(2)On the basis of possibility theory,the upper and lower possibility theory is introduced,and relevant numerical characteristics' formulas of trapezoidal fuzzy number are derived.Then multi-period mean-variance portfolio models with given exit time and transaction costs are constructed.Moreover,two improved algorithms for solving nonlinear programming problems are proposed,and we take a real example to show that: the upper and lower possibility theory reduces the computational load of the traditional mean-variance model to a certain extent when the profit is a fuzzy trapezoid number;the performance of the combination of genetic algorithm and the method for solving nonlinear programming is better than either method.The model also sets three constraint levels of return and risk to provide schemes for different investors.(3)Based on general fuzzy number,a novel fuzzy number is defined,and its numerical characteristics' formulas are derived based on the possibility theory.Then the specific formulas of trapezoidal and Gaussian fuzzy numbers' numerical characteristics are derived.In the case of trapezoidal fuzzy number,we define the number addition,number multiplication and fuzzy addition of the novel fuzzy number,and then prove some properties of novel fuzzy number's numerical characteristics,which ensure the theoretical feasibility of the portfolio model included the novel fuzzy numbers and its application.(4)In the fuzzy portfolio model,we use the novel fuzzy number to quantify the impact of uncertain exit time on asset returns,and add possibility entropy to measure the degree of investment diversification.Firstly,a single-period model is constructed,and then transaction cost is added to construct the multi-period possibility mean-variance-entropy model under uncertain exit time.Then we derive the concrete formulas when assets' return are three specific distributions,and illustrate the feasibility of the model in numerical examples with the method of fuzzy convex programming.In addition,we add the parameters of investors' exit willingness,preference for risk or investment diversification into the model,which provides suitable investment schemes for various types of investors.In conclusion,this dissertation puts forward a novel fuzzy number,constructs multi-period possibilistic portfolio models with given or uncertain exit time,and makes empirical analyses.These enrich the theory of fuzzy portfolio selection and have certain practical significance.