THE SKEWNESS FOR UNCERTAIN RANDOM VARIABLE AND APPLICATION TO PORTFOLIO SELECTION PROBLEM

Uncertainty and randomness are two basic types of indeterminacy, where uncertain variable is used to represent quantities with human uncer-tainty and random variable is applied for modeling quantities with objective randomness. In many real systems, uncertainty and randomness often exist simultaneously. Then uncertain random variable and chance measure can be used to handle such cases. We know that the skewness is a measure of distri-butional asymmetry. However, the concept of skewness for uncertain random variable has not been clearly defined. In this paper, we first propose a con-cept of skewness for uncertain random variable and then present a formula for calculating the skewness via chance distribution. Applying the presented for-mula, the skewnesses of three special uncertain random variables are derived. Finally, a portfolio selection problem is carried out for showing the efficiency and applicability of skewness and presented formula.

Automated summary

This paper proposes the concept of skewness for uncertain random variables and presents a formula for calculating skewness. By applying this formula, the skewnesses of three special uncertain random variables are derived. Finally, the efficiency and applicability of skewness and the presented formula are demonstrated through a portfolio selection problem.