Multivariate extremes and the aggregation of dependent risks: examples and counter-examples

DOI10.1007/s10687-008-0071-5zbMath1224.91057OpenAlexW2095295425MaRDI QIDQ626283

Mario V. Wüthrich, Paul Embrechts, Dominik D. Lambrigger

Publication date: 22 February 2011

Published in: Extremes (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/20.500.11850/20786

zbMATH Keywords

spectral measurevalue-at-risksubadditivitytail dependencerisk aggregationmultivariate regular variationmultivariate extreme value theory

Mathematics Subject Classification ID

Related Items (54)

Value-at-Risk, Tail Value-at-Risk and upper tail transform of the sum of two counter-monotonic random variables ⋮ Diversification limit of quantiles under dependence uncertainty ⋮ Risk Measures and Multivariate Extensions of Breiman's Theorem ⋮ The general tail dependence function in the Marshall-Olkin and other parametric copula models with an application to financial time series ⋮ Uniform asymptotics for a multi-dimensional time-dependent risk model with multivariate regularly varying claims and stochastic return ⋮ Risk in a Large Claims Insurance Market with Bipartite Graph Structure ⋮ Asymptotic ruin probabilities for a multidimensional renewal risk model with multivariate regularly varying claims ⋮ Bounds for randomly shared risk of heavy-tailed loss factors ⋮ Heavy tails and copulas: limits of diversification revisited ⋮ Asymptotic analysis of portfolio diversification ⋮ Spectral Density Ratio Models for Multivariate Extremes ⋮ Strength of tail dependence based on conditional tail expectation ⋮ Ordering of multivariate risk models with respect to extreme portfolio losses ⋮ Lévy Copulas: Review of Recent Results ⋮ THEORETICAL SENSITIVITY ANALYSIS FOR QUANTITATIVE OPERATIONAL RISK MANAGEMENT ⋮ Asymptotic subadditivity/superadditivity of Value‐at‐Risk under tail dependence ⋮ Diversification quotients based on VaR and ES ⋮ Risk concentration of aggregated dependent risks: the second-order properties ⋮ Estimating asymptotic dependence functionals in multivariate regularly varying models ⋮ Risk concentration under second order regular variation ⋮ Tail behavior of discounted portfolio loss under upper tail comonotonicity ⋮ Asymptotics of sum of heavy-tailed risks with copulas ⋮ Asymptotic behavior of tail distortion risk measure for aggregate weight-adjusted losses ⋮ Interplay of insurance and financial risks in a stochastic environment ⋮ Practices and issues in operational risk modeling under Basel II ⋮ Second-order properties of risk concentrations without the condition of asymptotic smoothness ⋮ Second-order expansions of the risk concentration based on CTE ⋮ Tail comonotonicity: properties, constructions, and asymptotic additivity of risk measures ⋮ On optimal portfolio diversification with respect to extreme risks ⋮ Simple risk measure calculations for sums of positive random variables ⋮ Second-order asymptotics of the risk concentration of a portfolio with deflated risks ⋮ Regular variation, conditions of domain of attraction and the existence of the tail dependence function in the general dependence case: a copula approach ⋮ Dependence structure of risk factors and diversification effects ⋮ Risk concentration and diversification: second-order properties ⋮ Upper bounds on value-at-risk for the maximum portfolio loss ⋮ Normex, a new method for evaluating the distribution of aggregated heavy tailed risks ⋮ Risk concentration based on expectiles for extreme risks under FGM copula ⋮ Extremes for multivariate expectiles ⋮ Fat tails, VaR and subadditivity ⋮ Revisiting the Edge, Ten Years On ⋮ Asymptotic Analysis of the Loss Given Default in the Presence of Multivariate Regular Variation ⋮ Counterdiagonal/nonpositive tail dependence in vine copula constructions: application to portfolio management ⋮ Rectangular Patchwork for Bivariate Copulas and Tail Dependence ⋮ Implementing loss distribution approach for operational risk ⋮ Backtesting extreme value theory models of expected shortfall ⋮ Asymptotics for ultimate ruin probability in a by-claim risk model ⋮ Bounds for the sum of dependent risks having overlapping marginals ⋮ On additivity of tail comonotonic risks ⋮ On sums of two counter-monotonic risks ⋮ Distributionally robust inference for extreme value-at-risk ⋮ Toward a Copula Theory for Multivariate Regular Variation ⋮ DIVERSIFICATION IN CATASTROPHE INSURANCE MARKETS ⋮ Nonparametric estimation of general multivariate tail dependence and applications to financial time series ⋮ Four theorems and a financial crisis

Uses Software

• QRM

Cites Work

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• On optimal portfolio diversification with respect to extreme risks
• An introduction to copulas.
• Modelling total tail dependence along diagonals
• High risk scenarios and extremes. A geometric approach
• Additivity properties for value-at-risk under archimedean dependence and heavy-tailedness
• Limit theory for bilinear processes with heavy-tailed noise
• Tail asymptotics for the sum of two heavy-tailed dependent risks
• Copulas: Tales and facts (with discussion)
• The Extremal Dependence Measure and Asymptotic Independence
• On the Tail Behavior of Sums of Dependent Risks
• Multivariate extremes, aggregation and dependence in elliptical distributions
• Statistics of Extremes
• Heavy-Tail Phenomena
• Regularly varying functions

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