2019/04/01 by Jaakko Lehtomaa, Lehtomaa, Jaakko, Sidney I. Resnick +1 · 1 citation
Economics, Econometrics and Finance · Mathematics · #60G70 #60K10 #62F05 #62G32 #90A46 #91B30 #Advanced Statistical Methods and Models #FOS: Mathematics #Financial Risk and Volatility Modeling #Statistical Methods and Inference #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.1904.00917
openalex publication_date 2019/04/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
One of the central objectives of modern risk management is to find a set of\nrisks where the probability of multiple simultaneous catastrophic events is\nnegligible. That is, risks are taken only when their joint behavior seems\nsufficiently independent. This paper aims to help to identify asymptotically\nindependent risks by providing additional tools for describing dependence\nstructures of multiple risks when the individual risks can obtain very large\nvalues.\n The study is performed in the setting of multivariate regular variation. We\nshow how asymptotic independence is connected to properties of the support of\nthe angular measure and present an asymptotically consistent estimator of the\nsupport. The estimator generalizes to any dimension N\≥ 2 and requires no\nprior knowledge of the support. The validity of the support estimate can be\nrigorously tested under mild assumptions by an asymptotically normal test\nstatistic.\n