Fuzzy Random Multiobjective Decision Making Models And Its Applications To Portfolio Selection

Among types of uncertainty surrounding real life problems, randomness (stochastic variation) and fuzziness (vagueness) play a pivotal role. Randomness is one type of uncertainty that describes occurrence of affairs, and random variables are used to describe the stochastic phenomena. Fuzzyness is one type of uncertainty that describes the uncertain state of affairs, and fuzzy sets are used to describe fuzzy phenomena. Accordingly, stochastic programming and fuzzy programming have been proposed to make decision under uncertainty environment. However, in a decision-making process, we may face a hybrid uncertain environment where fuzziness and randomness coexist. In such cases, the concept of fuzzy random variable is a useful tool dealing with the two types of uncertainty simultaneously. Roughly speaking, a fuzzy random variable is a measurable function from a probability space to the set of fuzzy variables. In other words, a fuzzy random variable is a random variable taking fuzzy values. Fuzzy random phenomena are existed extensively in real life problems. Therefore, research on fuzzy random multiobjective decision making bear not only academic but also practical significance.Portfolio selection theory deals with how to distribute investment money among different assets to maximize return as well as minimize risk. There are many kinds of uncertainty including randomness and fuzziness simultaneously in the stock market. So far, on the assumption that the future return rate of each securities is a random variable, most of the portfolio selection models are based on probability theory. Recently, fuzziness existed in the stock market are gradually recognized by some scholars. Several fuzzy portfolio selection models have been proposed on the assumption that the return rate of each securities is a fuzzy variable. Actually, either the stochastic portfolio selection models or fuzzy portfolio selection models consider only one type of uncertainty. Therefore, portfolio selection under hybrid uncertain environment needs further research.Hence, with summarizing the known researches on fuzzy random programming and portfolio selection models, we discuss the fuzzy random multiobjective programming models and algorithms based on the fuzzy random theory in this dissertation. By using fuzzy random variable to describe the fuzzy random phenomena existed in the stock market, we propose several portfolio selection models as well as multiobjective portfolio selection models under fuzzy random environment. The major achievements in this dissertation are listed as follows:(1) In order to characterize the randomness and fuzziness existed in the stock market simultaneously, the return rate of each securities is treated as a fuzzy random variable. The historical data, the experts' knowledge and experience as well as the investor's individual expectation about the return rate of each securities are considered in this disseration.(2) Following the mean variance principle, the fuzzy randomλ-mean variance model is proposed. Theλ-mean variance efficient frontier and theλ-mean variance efficient solution are defined, and the relations between theλ-mean variance efficient solutions located on differentλ-mean variance efficient frontiers are also discussed. The same expectation assumption on the future return rate of each securities, which is a basic assumption in Markowitz's mean-variance model, is no longer necessary, different investors can built their different portfolio selection models and therefore obtain their optimal investment strategy from the the proposed fuzzy randomλ-mean variance model. Furthermore, with the collection of historical data practical analysis is carried out for the proposed portfolio selection model. (3) Non-standard investors always consider more objectives besides return and risk, such as liquidity. Suppose that a investor consider return, risk and liquidity simultaneously, a constrained multiobjective portfolio selection model under fuzzy random environment is proposed, and the compromised-based genetic algorithm is used to obtain a compromise investment strategy.(4) Based on the fuzzy random chance constrained multiobjective programming model proposed by Liu, some crisp equivalent models are given for some special kinds of fuzzy random variables. For the general kinds of fuzzy random variables, hybrid intelligent algorithms which combine fuzzy random simulation and compromised-based genetic algorithms are combined together to propose a hybrid intelligent algorithm and therefore a compromised solution can be obtained.(5) Similar to the probability maximization model in stochastic programming, a class of fuzzy random chance maximization multiobjective programming model based on the primitive chance of fuzzy random event is proposed. For a special kind of fuzzy random variables, the crisp equivalent models are proposed and a method is also proposed to obtain a weakly efficient solution. For general kinds of fuzzy random variables, hybrid intelligent algorithm which combines fuzzy random simulation and compromised-based genetic algorithms is also designed to obtain a compromised solution.(6) Similar to the safety first model, fuzzy random chance maximization portfolio selection model and fuzzy random chance constrained portfolio selection model are proposed. Moreover, with the collection of historical data practical analysis is carried out to verify the effectiveness of the proposed models.(7) The interval goal programming is discussed from the view of interval orders and it is converted into a linear programming problem at last. By using the absolute deviation risk function, a portfolio selection model with interval return and interval absolute deviation is proposed based on the interval goal programming model. Moreover, with the collection of historical data practical analysis is carried out to verify the effectiveness of the proposed model. (8) The fuzzy random portfolio selection models proposed in this dissertation are compared with some of the existing stochastic and fuzzy portfolio selection models in literature.Based on fuzzy random theory, the fuzzy random multiobjective programming models, its traditional algorithms and hybrid intelligent algorithms are discussed in this dissertation. Moreover, the fuzzy random portfolio selection models, its algorithms and practical analysis are also discussed. Undoubtedly, these researches included in the dissertation are helpful to develop, improve and prompt the researches on fuzzy random multiobjective programming and fuzzy random portfolio selection models.