Coherence and elicitability
AbstractThe risk of a financial position is usually summarized by a risk measure. As this risk measure has to be estimated from historical data, it is important to be able to verify and compare competing estimation procedures. In statistical decision theory, risk measures for which such verification and comparison is possible, are called elicitable. It is known that quantile based risk measures such as value at risk are elicitable. In this paper we show that law-invariant spectral risk measures such as expected shortfall are not elicitable unless they reduce to minus the expected value. Hence, it is unclear how to perform forecast verification or comparison. However, the class of elicitable law-invariant coherent risk measures does not reduce to minus the expected value. We show that it contains expectiles, and that they play a special role amongst all elicitable law-invariant coherent risk measures.
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Bibliographic InfoPaper provided by arXiv.org in its series Papers with number 1303.1690.
Date of creation: Mar 2013
Date of revision: Mar 2013
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Web page: http://arxiv.org/
This paper has been announced in the following NEP Reports:
- NEP-ALL-2013-03-09 (All new papers)
- NEP-RMG-2013-03-09 (Risk Management)
- NEP-UPT-2013-03-09 (Utility Models & Prospect Theory)
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