A Portfolio Selection Model Based on the Interval Number

Abstract

Traditional portfolio theory uses probability theory to analyze the uncertainty of financial market. The assets’ return in a portfolio is regarded as a random variable which follows a certain probability distribution. However, it is difficult to estimate the assets return in the real financial market, so the interval distribution of asset return can be estimated according to the relevant suggestions of experts and decision makers, that is, the interval number is used to describe the distribution of asset return. Therefore, this paper establishes a portfolio selection model based on the interval number. In this model, the semiabsolute deviation risk function is used to measure the portfolio’s risk, and the solution of the model is obtained by using the order relation of the interval number. At the same time, a satisfactory solution of the model is obtained by using the concept of acceptability of the interval number. Finally, an example is given to illustrate the practicability of the model.