Tail asymptotic expansions for L-statistics

Hashorva, Enkelejd; Ling, Chengxiu; Peng, Zuoxiang

doi:10.1007/s11425-014-4841-z

Cited by 7 publications

(4 citation statements)

References 29 publications

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“…For a portfolio of i.i.d. risks, the second-order approximations of the risk concentrations VaR ( ), CTE ( ) as ↑ 1 have been discussed by Hashorva et al [24], while Mao and Yang [25] consider the case with a portfolio of dependent risks under FGM copula. Ling and Peng [26] derived higher-order approximations under some conditions.…”

Section: Introductionmentioning

confidence: 99%

Second-Order Asymptotics of the Risk Concentration of a Portfolio with Deflated Risks

Chen

Gao

et al. 2018

Mathematical Problems in Engineering

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The quantification of diversification benefits due to risk aggregation has received more attention in the recent literature. In this paper, we establish second-order asymptotics of the risk concentration based on several risk measures for a portfolio of identically distributed but dependent deflated risks = , = 1, 2, . . . , under the assumptions of second-order regular variation on the survival functions of the risks and the deflator , where 1 , 2 , . . . , are independent and identically distributed random variables with a common survival function and is a random variable being independent of 1 , 2 , . . . , . Examples are also given to illustrate our main results.

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Section: Introductionmentioning

confidence: 99%

Second-Order Asymptotics of the Risk Concentration of a Portfolio with Deflated Risks

Chen

Gao

et al. 2018

Mathematical Problems in Engineering

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“…It is useful to note that a variant of Conditional Tail Expectation (CTE) has the same representation like MES. CTE asymptotic approximations have appeared in various forms in the insurance and actuarial literature; Joe and Li (2011) focuses on distributions satisfying the multivariate regularly varying property, Hua and Joe (2011) and Zhu and Li (2012) investigate the same problem for scaled mixtures and multivariate elliptical distributions, while Hashorva et al (2014) consider dependence models that exhibit the second order regularly varying tail property. The same problem is discussed in Asimit et al (2011) for a variety of asymptotic dependence models, emphasizing that these extreme CTEs are useful when the total regulatory capital (based on TVaR) is allocated amongst many subsidiaries/lines of business (LOBs).…”

Section: Introductionmentioning

confidence: 99%

Extremes for coherent risk measures

Asimit

2016

Insurance: Mathematics and Economics

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This is the accepted version of the paper.This version of the publication may differ from the final published version. Permanent repository link: http://openaccess.city.ac.uk/16268/ Link to published version: http://dx.Abstract. Various concepts appeared in the existing literature to evaluate the risk exposure of a financial or insurance firm/subsidiary/line of business due to the occurrence of some extreme scenarios. Many of those concepts, such as Marginal Expected Shortfall or Tail Conditional Expectation, are simply some conditional expectations that evaluate the risk in adverse scenarios and are useful for signaling to a decision-maker the poor performance of its risk portfolio or to identify which sub-portfolio is likely to exhibit a massive downside risk. We investigate the latter risk under the assumption that it is measured via a coherent risk measure, which obviously generalizes the idea of only taking the expectation of the downside risk. Multiple examples are given and our numerical illustrations show how the asymptotic approximations can be used in the capital allocation exercise. We have concluded that the expectation of the downside risk does not fairly take into account the individual risk contribution when allocating the VaR-based regulatory capital, and thus, more conservative risk measurements are recommended. Finally, we have found that more conservative risk measurements do not improve the fairness of the cost of capital allocation when the uncertainty with parameter estimation is present, even at a very high level.

show abstract

Section: Introductionmentioning

confidence: 99%

Extremes for Coherent Risk Measures

Asimit

2016

SSRN Journal

View full text Add to dashboard Cite

Various concepts appeared in the existing literature to evaluate the risk exposure of a financial or insurance firm/subsidiary/line of business due to the occurrence of some extreme scenarios. Many of those concepts, such as Marginal Expected Shortfall or Tail Conditional Expectation, are simply some conditional expectations that evaluate the risk in adverse scenarios and are useful for signaling to a decision-maker the poor performance of its risk portfolio or to identify which sub-portfolio is likely to exhibit a massive downside risk. We investigate the latter risk under the assumption that it is measured via a coherent risk measure, which obviously generalizes the idea of only taking the expectation of the downside risk. Multiple examples are given and our numerical illustrations show how the asymptotic approximations can be used in the capital allocation exercise. We have concluded that the expectation of the downside risk does not fairly take into account the individual risk contribution when allocating the VaR-based regulatory capital, and thus, more conservative risk measurements are recommended. Finally, we have found that more conservative risk measurements do not improve the fairness of the cost of capital allocation when the uncertainty with parameter estimation is present, even at a very high level.

show abstract

Tail asymptotic expansions for L-statistics

Cited by 7 publications

References 29 publications

Second-Order Asymptotics of the Risk Concentration of a Portfolio with Deflated Risks

Second-Order Asymptotics of the Risk Concentration of a Portfolio with Deflated Risks

Extremes for coherent risk measures

Extremes for Coherent Risk Measures

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