Coherence and Elicitability

Ziegel, Johanna F.

doi:10.1111/mafi.12080

Cited by 294 publications

(183 citation statements)

References 39 publications

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“…The academic response to this fact is not unanimous: while ES is coherent and takes into consideration the whole tail distribution, it lacks some nice statistical properties characteristic to V@R. See e.g. Cont et al (2010); Acerbi and Székely (2014); Ziegel (2016); Kellner and Rösch (2016); Yamai and Yoshiba (2005); Emmer et al (2015) for further details and interesting discussions. Also, the ES forecasts are believed to be much harder to backtest, a property essential from the regulator's point of view.…”

Section: Introductionmentioning

confidence: 99%

“…In Section 7.1 we provide a detailed discussion of this topic. The lack of elicitability led to the discussion whether or not (and how) it is possible to backtest ES and we refer to Carver (2014); Ziegel (2016); Acerbi and Székely (2014); Fissler et al (2015) for further details on this topic. Quite recently it was shown in Fissler et al (2015) that ES is however jointly elicitable with V@R.…”

Section: Introductionmentioning

confidence: 99%

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Unbiased Estimation of Risk

Pitera

Schmidt

2016

SSRN Journal

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Abstract. The estimation of risk measures recently gained a lot of attention, partly because of the backtesting issues of expected shortfall related to elicitability. In this work we shed a new and fundamental light on optimal estimation procedures of risk measures in terms of bias. We show that once the parameters of a model need to be estimated, one has to take additional care when estimating risks. The typical plug-in approach, for example, introduces a bias which leads to a systematic underestimation of risk.In this regard, we introduce a novel notion of unbiasedness to the estimation of risk which is motivated by economic principles. In general, the proposed concept does not coincide with the wellknown statistical notion of unbiasedness. We show that an appropriate bias correction is available for many well-known estimators. In particular, we consider value-at-risk and expected shortfall (tail value-at-risk). In the special case of normal distributions, closed-formed solutions for unbiased estimators can be obtained.We present a number of motivating examples which show the outperformance of unbiased estimators in many circumstances. The unbiasedness has a direct impact on backtesting and therefore adds a further viewpoint to established statistical properties.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Unbiased Estimation of Risk

Pitera

Schmidt

2016

SSRN Journal

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“…Thus, we focus on the statistical robustness of the risk measurement procedure and in doing so complement recent approaches to evaluate model risk as in [7] or to use statistical concepts to evaluate the performance of risk measures as suggested in e.g., [8] or [9].…”

Section: Introductionmentioning

confidence: 99%

The Wasserstein Metric and Robustness in Risk Management

Kiesel

Rühlicke

Stahl³

et al. 2016

Risks

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Abstract:In the aftermath of the financial crisis, it was realized that the mathematical models used for the valuation of financial instruments and the quantification of risk inherent in portfolios consisting of these financial instruments exhibit a substantial model risk. Consequently, regulators and other stakeholders have started to require that the internal models used by financial institutions are robust. We present an approach to consistently incorporate the robustness requirements into the quantitative risk management process of a financial institution, with a special focus on insurance. We advocate the Wasserstein metric as the canonical metric for approximations in robust risk management and present supporting arguments. Representing risk measures as statistical functionals, we relate risk measures with the concept of robustness and hence continuity with respect to the Wasserstein metric. This allows us to use results from robust statistics concerning continuity and differentiability of functionals. Finally, we illustrate our approach via practical applications.

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“…For a general convex distribution-based risk measure ρ, the question of elicitability was studied, e.g., in Gneiting (2011), Ziegel (2014, Embrechts & Hofert (2014), Emmer, Kratz & Tasche (2013, Kou & Peng (2014), Bellini & Bignozzi (2014) and Bellini, Klar, Müller & Rosazza Gianin (2014). In this section we describe the main results.…”

Section: Elicitabilitymentioning

confidence: 99%

The Axiomatic Approach to Risk Measures for Capital Determination

Föllmer

Weber

2015

Annu. Rev. Financ. Econ.

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The quantification of downside risk in terms of capital requirements is a key issue for both regulators and the financial industry. This review presents the axiomatic approach, which is based on monetary risk measures. These provide a unifying mathematical framework for the determination of capital requirements, for economic indices of riskiness, and for the analysis of preferences in the face of risk and Knightian uncertainty. In the special case of distribution-based risk measures, we review recent advances in characterizing their statistical properties such as elicitability and robustness.

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Coherence and Elicitability

Cited by 294 publications

References 39 publications

Unbiased Estimation of Risk

Unbiased Estimation of Risk

The Wasserstein Metric and Robustness in Risk Management

The Axiomatic Approach to Risk Measures for Capital Determination

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