Comparing possibilistic portfolios to probabilistic ones

In this contribution, we compare mean-variance portfolios based on the standard probabilistic representation of the stock returns to mean-variance portfolios built by using stock returns represented as possibilistic numbers. There exists only a definition for the probabilistic mean and only one for the probabilistic variance, whereas there exist several definitions of possibilistic mean and of possibilistic variance. With reference to the latter, in this note we focus our attention on the definitions recently proposed in literature for modeling portfolio selection problems: the lower possibilistic mean and variance ([3]), the upper possibilistic mean and variance ([3]), and the possibilistic mean and variance `a la Zhang-Zhang-Xiao ([4]), hereinafter referred to as ZZX possibilistic mean and variance