Mean-risk model for portfolio selection with uncertain returns

The mean-variance model proposed by Markowitz has received greatly acceptance as a practical methodology to manage portfolio selection, and has been widely extended in a variety of literatures. The aim of this paper is to extend the mean-variance model in uncertain decision systems. We present a new mean-TVaR model for portfolio selection when the returns of securities are described as uncertain variables. When the returns of the securities are characterized as some special uncertain variables such as linear uncertain variables, zigzag uncertain variables and normal uncertain variables, we employ the formulas of mean and TVaR to turn the mean-TVaR model to its equivalent problem. Since the crisp equivalent model is a linear programming, it can be solved by some convenient optimization algorithms such as interior point algorithm and simplex algorithm, or directly by some optimization software. Finally, we present a portfolio selection problem of fermenting foods to demonstrate the modeling idea and the eectiveness of the method.