Coherence and Elicitability

Ziegel, Johanna F. (2016). Coherence and Elicitability. Mathematical Finance, 26(4), pp. 901-918. Wiley 10.1111/mafi.12080

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The 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, the existing result of the nonelicitability of expected shortfall is extended to all law-invariant spectral risk measures 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 consists of certain expectiles.

Item Type:

Journal Article (Original Article)

Division/Institute:

08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematical Statistics and Actuarial Science

UniBE Contributor:

Ziegel, Johanna F.

Subjects:

300 Social sciences, sociology & anthropology > 360 Social problems & social services
500 Science > 510 Mathematics

ISSN:

1467-9965

Publisher:

Wiley

Language:

English

Submitter:

Lutz Dümbgen

Date Deposited:

19 Nov 2015 09:35

Last Modified:

25 Apr 2017 23:42

Publisher DOI:

10.1111/mafi.12080

BORIS DOI:

10.7892/boris.73009

URI:

https://boris.unibe.ch/id/eprint/73009

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