On the Coherent Risk Measure Representations in the Discrete Probability Spaces

Abstract: 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.