Conditional excess risk measures and multivariate regular variation

Das Bikramjit () and Fasen-Hartmann Vicky ()
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Das Bikramjit: Engineering Systems and Design, Singapore University of Technology and Design, 8 Somapah Road, Singapore487372, Singapore
Fasen-Hartmann Vicky: Department of Mathematics, Karlsruhe Institute of Technology, Englerstr. 2, 76131Karlsruhe, Germany

Statistics & Risk Modeling, 2019, vol. 36, issue 1-4, 1-23

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.

Keywords: Copula models; expected shortfall; heavy-tails; hidden regular variation; mean excess; multivariate regular variation; systemic risk (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1515/strm-2018-0030

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