Mean-CVaR portfolio optimization is an alternative to the more widely known and simpler mean-variance model. Since there doesn't seem to be any median-variance model out there, the familiarity surrounding the traditional model stuck.
The mean is an actual equation with convenient properties in statistics, whereas the median is obtained through a counting procedure. The use of median asset returns is absent in finance, even though estimates of mean asset returns have been shown to be unreliable.
Does calculating median asset returns as an input drastically improve the portfolio solution enough from the usual mean asset returns to write a whole paper on the topic?
Robust statistics and resistant regression models often use estimators based on the median instead of the mean, and the absolute loss function instead of the widely used squared loss function, so you have a good point anyway.
