A portfolio selection model with interval-valued return rates

This paper mainly proposes a new model for stock markets, namely a portfolio selection model with interval-valued return rates. To do it, we review some concepts of interval numbers and the acceptability function of rankings at first. And we present an improved ranking method for intervals. Then, we introduce set-valued random variables, the semi-variance and the semi-covariance of interval-valued random variables and prove some related properties. After the preparation, we introduce our new portfolio selection model of interval-valued return rates with semi-variances as risk measurements of stocks. Finally, we do an empirical analysis by using real stock data in NASDAQ stock market to illustrate our model.