  We give a complete characterization of both comonotone and not comonotone
coherent risk measures in the discrete finite probability space, where each
outcome is equally likely. To the best of our knowledge, this is the first work
that characterizes \textit{and} distinguishes comonotone and not comonotone
coherent risk measures via a simplified AVaR representation in this probability
space, which is crucial in applications and simulations.
