Additivity properties for Value-at-Risk under Archimedean dependence and heavy-tailedness

Paul Embrechts; Johanna Nešlehová; Mario V. Wüthrich

doi:10.1016/j.insmatheco.2008.08.001

Additivity properties for Value-at-Risk under Archimedean dependence and heavy-tailedness

Paul Embrechts
, Johanna Nešlehová
, Mario V. Wüthrich^*

^*Corresponding author for this work

Publication: Scientific journal › Journal article › peer-review

Abstract

Mainly due to new capital adequacy standards for banking and insurance, an increased interest exists in the aggregation properties of risk measures like Value-at-Risk (VaR). We show how VaR can change from sub to superadditivity depending on the properties of the underlying model. Mainly, the switch from a finite to an infinite mean model gives a completely different asymptotic behaviour. Our main result proves a conjecture made in Barbe et al. [Barbe, P., Fougères, A.L., Genest, C., 2006. On the tail behavior of sums of dependent risks. ASTIN Bull. 36(2), 361-374].

Original language	English
Pages (from-to)	164-169
Number of pages	6
Journal	Insurance: Mathematics and Economics
Volume	44
Issue number	2
DOIs	https://doi.org/10.1016/j.insmatheco.2008.08.001
Publication status	Published - Apr 2009
Externally published	Yes

Keywords

Aggregation
Archimedean copula
Dependence structure
Subadditivity
Value-at-Risk

Access to Document

10.1016/j.insmatheco.2008.08.001

Cite this

@article{e1d9d86388db4d7883e1b67665dda2be,

title = "Additivity properties for Value-at-Risk under Archimedean dependence and heavy-tailedness",

abstract = "Mainly due to new capital adequacy standards for banking and insurance, an increased interest exists in the aggregation properties of risk measures like Value-at-Risk (VaR). We show how VaR can change from sub to superadditivity depending on the properties of the underlying model. Mainly, the switch from a finite to an infinite mean model gives a completely different asymptotic behaviour. Our main result proves a conjecture made in Barbe et al. [Barbe, P., Foug{\`e}res, A.L., Genest, C., 2006. On the tail behavior of sums of dependent risks. ASTIN Bull. 36(2), 361-374].",

keywords = "Aggregation, Archimedean copula, Dependence structure, Subadditivity, Value-at-Risk",

author = "Paul Embrechts and Johanna Ne{\v s}lehov{\'a} and W{\"u}thrich, \{Mario V.\}",

year = "2009",

month = apr,

doi = "10.1016/j.insmatheco.2008.08.001",

language = "English",

volume = "44",

pages = "164--169",

journal = "Insurance: Mathematics and Economics",

issn = "0167-6687",

publisher = "Elsevier B.V.",

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TY - JOUR

T1 - Additivity properties for Value-at-Risk under Archimedean dependence and heavy-tailedness

AU - Embrechts, Paul

AU - Nešlehová, Johanna

AU - Wüthrich, Mario V.

PY - 2009/4

Y1 - 2009/4

N2 - Mainly due to new capital adequacy standards for banking and insurance, an increased interest exists in the aggregation properties of risk measures like Value-at-Risk (VaR). We show how VaR can change from sub to superadditivity depending on the properties of the underlying model. Mainly, the switch from a finite to an infinite mean model gives a completely different asymptotic behaviour. Our main result proves a conjecture made in Barbe et al. [Barbe, P., Fougères, A.L., Genest, C., 2006. On the tail behavior of sums of dependent risks. ASTIN Bull. 36(2), 361-374].

AB - Mainly due to new capital adequacy standards for banking and insurance, an increased interest exists in the aggregation properties of risk measures like Value-at-Risk (VaR). We show how VaR can change from sub to superadditivity depending on the properties of the underlying model. Mainly, the switch from a finite to an infinite mean model gives a completely different asymptotic behaviour. Our main result proves a conjecture made in Barbe et al. [Barbe, P., Fougères, A.L., Genest, C., 2006. On the tail behavior of sums of dependent risks. ASTIN Bull. 36(2), 361-374].

KW - Aggregation

KW - Archimedean copula

KW - Dependence structure

KW - Subadditivity

KW - Value-at-Risk

U2 - 10.1016/j.insmatheco.2008.08.001

DO - 10.1016/j.insmatheco.2008.08.001

M3 - Journal article

AN - SCOPUS:63449119587

SN - 0167-6687

VL - 44

SP - 164

EP - 169

JO - Insurance: Mathematics and Economics

JF - Insurance: Mathematics and Economics

IS - 2

ER -