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COHERENCE AND ELICITABILITY

COHERENCE AND ELICITABILITY 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Mathematical Finance Wiley

COHERENCE AND ELICITABILITY

Mathematical Finance , Volume 26 (4) – Oct 1, 2016

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References (42)

Publisher
Wiley
Copyright
© 2016 Wiley Periodicals, Inc.
ISSN
0960-1627
eISSN
1467-9965
DOI
10.1111/mafi.12080
Publisher site
See Article on Publisher Site

Abstract

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.

Journal

Mathematical FinanceWiley

Published: Oct 1, 2016

Keywords: ; ; ; ; ; ;

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