We introduce different ways of adjusting classical risk measures in different contexts. We mainly discuss the properties of a new class of convex risk measures that robustifies Expected Shortfall by simultaneously controlling the expected losses associated with different portions of the tail distribution. The key element is a benchmark risk profile g which allows, at the same time, to tailor the risk assessment to the specific application of interest. The resulting risk measure is intimately connected with second-order stochastic dominance. A second way of adjusting and robustifying risk measures is presented in a systemic risk framework which is not based on any probabilistic assumption.
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