The Study On Risk Criteria Of Semivariance And Its Application

Portfolio selection is concerned with the problem that how to allocate investors' wealth among alternative securities. The purpose of the investors is to obtain the maximum profit via diversitication of investment. However, the returns of the in-verstments are uncertain in practical market. In this thesis, we employ uncertainty theory to deal with this type of investment problem. Under this consideration, we employ fuzzy random theory to study the portfolio selection problem.According to the definition of fuzzy random variable, we first give the definition of semivariance of fuzzy random variable, and establish the semivariance formulas for triangular and trapezoidal fuzzy random variables. Then, on the basis of expecta-tion and semivariance, we build three classes of portfolio selection models with fuzzy random returns. According to the established semivariance formulas, the original fuzzy random portfolio problems can be reduced to their equivalent stochastic pro-gramming ones, which can be solved by conventional optimization software. Finally, we give two numerical examples to demonstrate the proposed modeling idea.The main contribution of this thesis contains the following four aspects:(ⅰ) The conception of semivariance of fuzzy random variables is defined and its properties are discussed; (ⅱ) The semivariance formulas for fuzzy random variables are deduced; (ⅲ) On the basis of expectation and semivariance, three new classes of portfolio models are esstablished, and the equivalent stochastic models are discussed; (ⅳ) Two numerical examples are provided to demonstrate the proposed modeling idea.