scholarly journals Evaluating Risk Measures and Capital Allocations Based on Multi-Losses Driven by a Heavy-Tailed Background Risk: The Multivariate Pareto-Ii Model

2013 ◽  
Author(s):  
Vali Alexandru Asimit ◽  
Raluca Vernic ◽  
Ricardas Zitikis
Keyword(s):  
Risk Measures ◽  
Background Risk ◽  
Heavy Tailed

ESTIMATION OF RISK MEASURES FROM HEAVY TAILED DISTRIBUTIONS

2021 ◽  
Vol 62 (1) ◽  
pp. 35-80
Author(s):  
El Hadji Deme ◽  
Mouhamad M. Allaya ◽  
Siradhi Deme ◽  
Hamza Dhaker ◽  
Ali Souleyman Dabye
Keyword(s):  
Risk Measures ◽  
Heavy Tailed Distributions ◽  
Heavy Tailed ◽  
Estimation Of Risk

Conditional excess risk measures and multivariate regular variation

2019 ◽  
Vol 36 (1-4) ◽  
pp. 1-23
Author(s):  
Bikramjit Das ◽  
Vicky Fasen-Hartmann
Keyword(s):  
Risk Factors ◽  
Asymptotic Behavior ◽  
Systemic Risk ◽  
Regular Variation ◽  
Risk Measures ◽  
Excess Risk ◽  
Multivariate Regular Variation ◽  
Marginal Expected Shortfall ◽  
Broad Framework ◽  
Heavy Tailed

Abstract Conditional excess risk measures like Marginal Expected Shortfall and Marginal Mean Excess are designed to aid in quantifying systemic risk or risk contagion in a multivariate setting. In the context of insurance, social networks, and telecommunication, risk factors often tend to be heavy-tailed and thus frequently studied under the paradigm of regular variation. We show that regular variation on different subspaces of the Euclidean space leads to these risk measures exhibiting distinct asymptotic behavior. Furthermore, we elicit connections between regular variation on these subspaces and the behavior of tail copula parameters extending previous work and providing a broad framework for studying such risk measures under multivariate regular variation. We use a variety of examples to exhibit where such computations are practically applicable.

scholarly journals Estimating -Functionals for Heavy-Tailed Distributions and Application

2010 ◽  
Vol 2010 ◽  
pp. 1-34 ◽  
Author(s):  
Abdelhakim Necir ◽  
Djamel Meraghni
Keyword(s):  
Asymptotic Normality ◽  
Extreme Value Theory ◽  
Financial Risk ◽  
Risk Measures ◽  
Value Theory ◽  
Statistical Parameters ◽  
Linear Combinations ◽  
Heavy Tailed Distributions ◽  
Heavy Tailed ◽  
Actuarial Risk

-functionals summarize numerous statistical parameters and actuarial risk measures. Their sample estimators are linear combinations of order statistics (-statistics). There exists a class of heavy-tailed distributions for which the asymptotic normality of these estimators cannot be obtained by classical results. In this paper we propose, by means of extreme value theory, alternative estimators for -functionals and establish their asymptotic normality. Our results may be applied to estimate the trimmed -moments and financial risk measures for heavy-tailed distributions.

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