Expected shortfall is jointly elicitable with value-at-risk: implications for backtesting

Fissler, Ziegel and Gneiting investigate the role of elicitability in backtesting problems and show how comparative backtests can be implemented for expected shortfall

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There continues to be lively debate about the appropriate choice of quantitative risk measure for regulatory purposes and internal risk management. In this context, it has been shown by Weber (2006) and Gneiting (2011) that expected shortfall (ES) is not elicitable. Specifically, there is no strictly consistent scoring (or loss) function.

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