The Credibility Theory And Its Application In Portfolio Selection

The thesis is divided into two parts. The first part is about credibility theory. Based on convergence in credibility measure, we introduce the definition of the strong law of large numbers for fuzzy variables, and by convergence almost sure, we present the concept of the weak law of large numbers for fuzzy variables. Then some sufficient conditions of the strong law of large numbers for L-R fuzzy variables and fuzzy variables with unbounded supports are discussed. In addition, we deduce the variance formulas of three common types of fuzzy variables and discuss their properties. The second part of the thesis is about the application of credibility theory. We employ credibility theory to study portfolio selection problem, and build three types of portfolio selection models in fuzzy environment. We provide three numerical examples for the proposed models and employ a genetic algorithm to solve them.The major new results of the thesis are summarized as the following four aspects:· The variance formulas of three common types of fuzzy variables are deduced and their properties are discussed;· The concepts of the strong law of large numbers and the weak law of large numbers for sequence of fuzzy variables are introduced;· The sufficient conditions of the strong law of large numbers for L-R fuzzy variables and fuzzy variables with unbounded supports are provided;· The application of credibility theory to portfolio selection problem is considered, three types of fuzzy portfolio selection models are presented, and the distributive investment solutions are obtained.