General lower bounds on convex functionals of aggregate sums

Cheung, Ka Chun; Lo, Ambrose

doi:10.1016/j.insmatheco.2013.10.005

Cited by 23 publications

(13 citation statements)

References 11 publications

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“…This risk measure was first introduced by Haezendonck and Goovaerts (1982) based on the Swiss premium calculation principle induced by the Orlicz norm and was revisited by Goovaerts et al (2004). Since recently, it has attracted increasing attention from researchers; see Rosazza Gianin (2008a,b, 2012), Krätschmer and Zähle (2011), Nam et al (2011), Goovaerts et al (2012), Mao and Hu (2012), Tang and Yang (2012), Cheung and Lo (2013) and Ahn and Shyamalkumar (2014), among others. As pointed out by Bellini and Rosazza Gianin (2012), the HG risk measure is a law invariant and coherent risk measure for a convex Young function ϕ(·).…”

Section: Introductionmentioning

confidence: 99%

Extreme value analysis of the Haezendonck–Goovaerts risk measure with a general Young function

Tang¹,

Yang²

2014

Insurance: Mathematics and Economics

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Section: Introductionmentioning

confidence: 99%

Extreme value analysis of the Haezendonck–Goovaerts risk measure with a general Young function

Tang¹,

Yang²

2014

Insurance: Mathematics and Economics

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“…A fast algorithm to numerically calculate the worst-case and best-case values of VaR under general conditions was introduced in Embrechts et al (2013). For the best-case ES, some partial analytical results can be found in Bernard et al (2014) and Cheung and Lo (2013), and a numerical procedure was proposed by Puccetti (2013).…”

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confidence: 99%

Aggregation-robustness and model uncertainty of regulatory risk measures

2015

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Research related to aggregation, robustness, and model uncertainty of regulatory risk measures, for instance, Value-at-Risk (VaR) and Expected Shortfall (ES), is of fundamental importance within quantitative risk management. In risk aggregation, marginal risks and their dependence structure are often modeled separately, leading to uncertainty arising at the level of a joint model. In this paper, we introduce a notion of qualitative robustness for risk measures, concerning the sensitivity of a risk measure to the uncertainty of dependence in risk aggregation. It turns out that coherent risk measures, such as ES, are more robust than VaR according to the new notion of robustness. We also give approximations and inequalities for aggregation and diversification of VaR under dependence uncertainty, and derive an asymptotic equivalence for worst-case VaR and ES under general conditions. We obtain that for a portfolio of a large number of risks VaR generally has a larger uncertainty spread compared to ES. The results warn that unjustified diversification arguments for VaR used in risk management need to be taken with much care, and potentially support the use of ES in risk aggregation. This in particular reflects on the discussions in the recent consultative documents by the Basel Committee on Banking Supervision.

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“…Lemma 3 gives a necessary and sufficient condition for the convex order of two random variables. The following lemma, due to Cheung and Lo [33], will play a crucial role in the proof of Theorem 2.…”

Section: Proof Of Theoremmentioning

confidence: 99%

Sharp Convex Bounds on the Aggregate Sums–An Alternative Proof

Yin

Zhu

2016

Risks

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Abstract:It is well known that a random vector with given marginals is comonotonic if and only if it has the largest convex sum, and that a random vector with given marginals (under an additional condition) is mutually exclusive if and only if it has the minimal convex sum. This paper provides an alternative proof of these two results using the theories of distortion risk measure and expected utility.

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General lower bounds on convex functionals of aggregate sums

Cited by 23 publications

References 11 publications

Extreme value analysis of the Haezendonck–Goovaerts risk measure with a general Young function

Extreme value analysis of the Haezendonck–Goovaerts risk measure with a general Young function

Aggregation-robustness and model uncertainty of regulatory risk measures

Sharp Convex Bounds on the Aggregate Sums–An Alternative Proof

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