Distortion risk measures for sums of random variables

Darkiewicz, Grzegorz; Dhaene, Jan; Goovaerts, Marc

doi:10.1007/bf02808970

Cited by 2 publications

(2 citation statements)

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“…According to (4), the computation of the DRM corresponding to Z, given in (2), requires the knowledge of the copula density and the margins of vector X. In particular, for the bivariate case (d = 2), we have…”

Section: Copula Representation Of the Drmmentioning

confidence: 99%

Distortion Risk Measures for Sums of Dependent Losses

Brahimi,

Meraghni,

Necir

2010

SSRN Journal

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We discuss two distinct approaches, for distorting risk measures of sums of dependent random variables, which preserve the property of coherence. The first, based on distorted expectations, operates on the survival function of the sum. The second, simultaneously applies the distortion on the survival function of the sum and the dependence structure of risks, represented by copulas. Our goal is to propose risk measures that take into account the fluctuations of losses and possible correlations between risk components.Résumé. Nous discutons deux approches distinctes, de distortion des mesures de risque de la somme de variables aléatoires dépendantes, qui conservent la propriété de cohérence. La première, basée sur les espérances distordues, agit sur la fonction de survie de la somme. La seconde, applique des déformations simultanées sur la fonction de survie de la somme et sur la structure de dépendance des risques, représentée par une copule. Notre objectif est de proposer des mesures qui prennent en compte les fluctuations des pertes et des corrélationséventuelles entre les composantes d'un risque multivarié.MSC 2010: 60B05, 62H20, 91B30.

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Section: Copula Representation Of the Drmmentioning

confidence: 99%

Distortion Risk Measures for Sums of Dependent Losses

Brahimi,

Meraghni,

Necir

2010

SSRN Journal

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“…Now, assume that X (1) , ..., X (d) are dependent with joint df H and continuous margins F i , i = 1, ..., d. In this case, the problem becomes different and its resolution requires more than the usual background. Several authors discussed the DRM, when applied to sums of rv's, against some classical dependency measures such as Person's r, Spearman's ρ and Kendall's τ, see for instance, Darkiewicz et al [4] and Burgert and Rüschendorf [2]. Our contribution is to introduce the copula notion to provide more flexibility to the DRM of sums of rv's in terms of loss and dependence structure.…”

Section: Introductionmentioning

confidence: 99%

Distortion risk measures for sums of dependent losses

Brahimi¹,

Meraghni²,

Necir³

2011

afst

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We discuss two distinct approaches, for distorting risk measures of sums of dependent random variables, which preserve the property of coherence. The first, based on distorted expectations, operates on the survival function of the sum. The second, simultaneously applies the distortion on the survival function of the sum and the dependence structure of risks, represented by copulas. Our goal is to propose risk measures that take into account the fluctuations of losses and possible correlations between risk components. Résumé. Nous discutons deux approches distinctes, de distortion des mesures de risque de la somme de variables aléatoires dépendantes, qui conservent la propriété de cohérence. La première, basée sur les espérances distordues, agit sur la fonction de survie de la somme. La seconde, applique des déformations simultanées sur la fonction de survie de la somme et sur la structure de dépendance des risques, représentée par une copule. Notre objectif est de proposer des mesures qui prennent en compte les fluctuations des pertes et des corrélationséventuelles entre les composantes d'un risque multivarié.

show abstract

Distortion risk measures for sums of random variables

Cited by 2 publications

References 5 publications

Distortion Risk Measures for Sums of Dependent Losses

Distortion Risk Measures for Sums of Dependent Losses

Distortion risk measures for sums of dependent losses

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