Before revision:  The main result is that the only tail risk measure that satisfies a set of economic axioms proposed by Schmeidler (1989, Econometrica) and the statistical property of elicitability (i.e. there exists an objective function such that minimizing the expected objective function yields the risk measure ;
After revision:  The main result is that the only tail risk measure that satisfies a set of economic axioms for the Choquet expected utility and the statistical property of elicitability (i.e. there exists an objective function such that minimizing the expected objective function yields the risk measure ;