The Study On Fuzzy Random Theory And Its Application In Portfolio Selection

Portfolio selection is concerned with the problem that how to allocate investors' wealth among alternative securities. The purpose of portfolio selection is to disperse risk so that the investors can obtain the maximum profit. However, in real-word problems, since the return rate of each asset depends on the changing securities business, sometimes investors have to deal with the hybrid uncertainty where lin-guistic and frequent nature coexist. In this thesis, we employ fuzzy random theory to study the portfolio selection problem in fuzzy random decision making systems.First of all, this thesis establishes the sufficient conditions for the continuity of equilibrium chance functions, and discusses some new analytical properties of the critical value functions. Then we deduce the variance formulas for triangular fuzzy random variables. At last, we employ fuzzy random theory to study portfolio selection problem, and build two classes of portfolio selection models. To solve the proposed portfolio problems, this thesis applies the variance formulas to the proposed models so that the original portfolio problems can be reduced to their equivalent stochastic programming ones, which can be solved by genetic algorithm (GA). To demonstrate the proposed models and methods, we provide two numerical examples, this thesis also verifies the obtained optimal solutions via K-T conditions.The main work of this thesis includes the following four aspects:(1) the suffi-cient conditions for the continuity of equilibrium chance functions are established; (2) some new analytical properties about equilibrium chance critical functions are discussed; (3) the variance formulas for triangular fuzzy random variables are de-duced; (4) the application of fuzzy random theory to portfolio selection problem is considered, two classes of fuzzy random portfolio selection models are presented, GA is designed to solve the equivalent stochastic models. Two numerical examples are given to demonstrate the proposed methods, and the obtained optimal solutions are verified via K-T conditions.