Uncertain random portfolio selection with high order moments

Abstract

<p style='text-indent:20px;'>In financial phenomena, investors are confronted with a hybrid uncertainty, where random and uncertain returns can occur simultaneously. This paper studies the kurtosis of an uncertain random variable and its application in portfolio selection. We are aware that the kurtosis measures the extreme values in each tail of the distribution. However, the notion of kurtosis for uncertain random variables has not been properly established. Thus, we introduce the concept of kurtosis of an uncertain random variable and extract some significant properties. Next, by invoking chance distribution we derive the kurtosis of three particular uncertain random variables, as well as the variance. Then, we present an uncertain random mean-variance-skewness-kurtosis portfolio selection model with their corresponding variations to meet various investors' requirements. Finally, two numerical examples are presented along with a comparative study to explain and illustrate the main results.</p>