Abstract
Tail risk refers to the risk associated with extreme values and is often affected by extremal dependence among multivariate extremes. Multivariate tail risk, as measured by a coherent risk measure of tail conditional expectation, is analyzed for multivariate regularly varying distributions. Asymptotic expressions for tail risk are established in terms of the intensity measure that characterizes multivariate regular variation. Tractable bounds for tail risk are derived in terms of the tail dependence function that describes extremal dependence. Various examples involving Archimedean copulas are presented to illustrate the results and quality of the bounds.
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Harry Joe is supported by NSERC Discovery Grant.
Haijun Li is supported in part by NSF grant CMMI 0825960.
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Joe, H., Li, H. Tail Risk of Multivariate Regular Variation. Methodol Comput Appl Probab 13, 671–693 (2011). https://doi.org/10.1007/s11009-010-9183-x
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DOI: https://doi.org/10.1007/s11009-010-9183-x