Elicitable Risk Measures

Bellini, F.; Bignozzi, Valeria

doi:10.2139/ssrn.2334746

Cited by 62 publications

(76 citation statements)

References 25 publications

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“…if two probability models P 1 , P 2 are such that VaR α X ; Gneiting, 2011 ). Further, VaR is monotone and translation invariant (see properties (a) and (b) from Section 2.3 ) and therefore, we can apply Lemma 2.2 in Bellini and Bignozzi (2015) to obtain that VaR is quasilinear. That is,…”

Section: Robustness Of Risk Measuresmentioning

confidence: 99%

Robust and Pareto Optimality of Insurance Contracts

et al. 2017

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a b s t r a c tThe optimal insurance problem represents a fast growing topic that explains the most efficient contract that an insurance player may get. The classical problem investigates the ideal contract under the assumption that the underlying risk distribution is known, i.e. by ignoring the parameter and model risks. Taking these sources of risk into account, the decision-maker aims to identify a robust optimal contract that is not sensitive to the chosen risk distribution. We focus on Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR)-based decisions, but further extensions for other risk measures are easily possible. The Worst-case scenario and Worst-case regret robust models are discussed in this paper, which have been already used in robust optimisation literature related to the investment portfolio problem. Closed-form solutions are obtained for the VaR Worst-case scenario case, while Linear Programming (LP) formulations are provided for all other cases. A caveat of robust optimisation is that the optimal solution may not be unique, and therefore, it may not be economically acceptable, i.e. Pareto optimal. This issue is numerically addressed and simple numerical methods are found for constructing insurance contracts that are Pareto and robust optimal. Our numerical illustrations show weak evidence in favour of our robust solutions for VaR-decisions, while our robust methods are clearly preferred for CVaR-based decisions.

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Section: Robustness Of Risk Measuresmentioning

confidence: 99%

Robust and Pareto Optimality of Insurance Contracts

et al. 2017

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“…According to [3], expectiles are the only coherent as well as elicitable risk measure. The expectiles were introduced in the context of statistical regression models by Newey and Powell in [24].…”

Section: Elicitability Of Risk Measuresmentioning

confidence: 99%

“…It is also examined in a purely mathematical framework in [34]. The elicitability of risk measures is further analyzed in [3] and [35]. Expectiles, as risk measures, were the subject of the works presented in [16], [5], and [4].…”

Section: Introductionmentioning

confidence: 99%

Multivariate extensions of expectiles risk measures

Maume-Deschamps

Rullière

Said

2017

Dependence Modeling

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“…ES is coherent (Acerbi and Tasche, 2002), but nevertheless fails to enjoy elicitability (Gneiting, 2011), another desired property of risk measures for which meaningful point forecasts and forecast performance comparisons are possible. Expectiles are the only risk measure that is both coherent and elicitable (Ziegel, 2016;Bellini and Bignozzi, 2015).…”

Section: Introductionmentioning

confidence: 99%

Aggregated Expectile Regression by Exponential Weighting

Zou

2018

STAT SINICA

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Various estimators have been proposed to estimate conditional expectiles, including those from the multiple linear expectile regression, local polynomial expectile regression, boosted expectile regression, and so on. It is common practice that several plausible candidate estimators are fitted and a final estimator is selected from the candidate list. In this article, we advocate the use of an exponential weighting scheme to adaptively aggregate the candidate estimators into a final estimator. We show oracle inequalities for the aggregated estimator.Simulations and real data examples demonstrate that the aggregated estimator could have substantial gain in accuracy under both the squared and asymmetric squared errors.

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Elicitable Risk Measures

Cited by 62 publications

References 25 publications

Robust and Pareto Optimality of Insurance Contracts

Robust and Pareto Optimality of Insurance Contracts

Multivariate extensions of expectiles risk measures

Aggregated Expectile Regression by Exponential Weighting

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