Svindland, GregorAhmed, ShabbirFilipovic, Damir2010-04-252010-04-252010-04-25200810.1016/j.orl.2008.06.009https://infoscience.epfl.ch/handle/20.500.14299/49708Recently Heyde, Kou and Peng (2007) proposed the notion of a natural risk statistic associated with a finite sample that relaxes the subadditivity assumption in the classical coherent risk statistics. In this note we use convex analysis to provide alternate proofs of the representation results regarding natural risk statistics.natural and coherent risk statistics, convex analysistext::journal::journal article::research article