Interval random dependent-chance programming and its application to portfolio selection

When employing fuzzy random variable in some real programming problems, it is not easy to specify the fuzzy values of random variables. But it is relatively easy to obtain the boundaries of the values of random variables. Hence, it is a good idea for people to determine the values of random variables as intervals. In this paper, we introduce the framework of interval random variable and interval random dependent-chance programming model. To pay attentions to both randomness and incompleteness of financial environment, we build the portfolio selection model by quantifying the stock return as interval random variable under this framework. Some computational results are discussed that demonstrate the potentially significant economic benefits of investing in portfolios computed using classical models and the model introduced here. The benefits are achieved at relatively high performance and low cost.