On the Identification of the Riskiest Directional Components from Multivariate Heavy-tailed Data

In insurance and finance, it is not uncommon to find heavy-tailed features in multivariate data sets. Since financial entities seek ways to reduce the total risks of their portfolios, it is necessary to understand what the main sources of risks are. Once this is known, one can seek optimal ways of reducing riskiness. In univariate data, there exist standard procedures for identifying dominating characteristics that produce the largest observations. However, in the multivariate setting, the situation is quite different. The study aims to provide tools and algorithms for detecting dominating directional components in multivariate data. We study general heavy-tailed multivariate random vectors and derive a presentation for the set of the riskiest directional components. We present consistent estimators which can be used in practical analysis to evaluate why the data is heavy-tailed. The results are of particular interest in insurance when setting reinsurance policies and in finance when hedging a portfolio of multiple assets.

Find the Q&A here: Q&A on 'Understanding Risks in Practice'