This paper attempts to provide a decision theoretical foundation for the measurement of economic tail risk, which is not only closely related to utility theory but also relevant to statistical model uncertainty. The main result of the paper is that the only tail risk measure that satisfies both 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; see Gneiting , 2011, J. Amer. Stat. Assoc.)  is median shortfall, which is the median of the tail loss distribution.  As an application, we argue that median shortfall is a better alternative than expected shortfall as a risk measure for setting capital requirements in Basel Accords.
This paper attempts to provide a decision-theoretic foundation for the measurement of economic tail risk, which is not only closely related to utility theory but also relevant to statistical model uncertainty. 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; see Gneiting ( 2011, J. Amer. Stat. Assoc.) ) is median shortfall, which is the median of tail loss distribution. Elicitability is important for backtesting. Median shortfall has a desirable property of distributional robustness with respect to model misspecification. We also extend the result to address model uncertainty by incorporating multiple scenarios. As an application, we argue that median shortfall is a better alternative than expected shortfall for setting capital requirements in Basel Accords.
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decision theoretical
decision-theoretic
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of the paper
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both
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,
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the
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Elicitability is important for backtesting. Median shortfall has a desirable property of distributional robustness with respect to model misspecification. We also extend the result to address model uncertainty by incorporating multiple scenarios.
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as a risk measure