On the Coherent Risk Measure Representations in the Discrete Probability Spaces

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 and distinguishes comonotone and not comonotone coherent risk measures via AVaR representation in the discrete finite probability space of equally likely atoms. The characterization gives a more efficient and exact way of representing the law invariant coherent risk measures in this probability space, which is crucial in applications and simulations.