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Quantification of multivariate risk
 Hilbert, Hynek ; Hlubinka, Daniel (advisor) ; Hudecová, Šárka (referee)
In the present work we study multivariate extreme value theory. Our main focus is on exceedances over linear thresholds. Smaller part is devoted to exce- edances over elliptical thresholds. We consider extreme values as those which belong to remote regions and investigate convergence of their distribution to the limit distribution. The regions are either halfspaces or ellipsoids. Working with halfspaces we distinguish between two setups: we either assume that the distribution of extreme values is directionally homogeneous and we let the halfspaces diverge in any direction, or we assume that there are some irre- gularities in the sample cloud which show us the fixed direction we should let the halfspaces drift out. In the first case there are three limit laws. The domains of attraction contain unimodal and rotund-exponential distributions. In the second case there exist a lot of limit laws without general form. The domains of attraction also fail to have common structure. The similar situation occurs for the exceedances over elliptical thresholds. The task here is to investigate convergence of the random vectors living in the complements of ellipsoids. For all, the limit distributions are determined by affine transformations and distribution of spectral measure. 1
Detailed record
Quantification of multivariate risk
 Hilbert, Hynek ; Hlubinka, Daniel (advisor) ; Hudecová, Šárka (referee)
In the present work we study multivariate extreme value theory. Our main focus is on exceedances over linear thresholds. Smaller part is devoted to exce- edances over elliptical thresholds. We consider extreme values as those which belong to remote regions and investigate convergence of their distribution to the limit distribution. The regions are either halfspaces or ellipsoids. Working with halfspaces we distinguish between two setups: we either assume that the distribution of extreme values is directionally homogeneous and we let the halfspaces diverge in any direction, or we assume that there are some irre- gularities in the sample cloud which show us the fixed direction we should let the halfspaces drift out. In the first case there are three limit laws. The domains of attraction contain unimodal and rotund-exponential distributions. In the second case there exist a lot of limit laws without general form. The domains of attraction also fail to have common structure. The similar situation occurs for the exceedances over elliptical thresholds. The task here is to investigate convergence of the random vectors living in the complements of ellipsoids. For all, the limit distributions are determined by affine transformations and distribution of spectral measure. 1
Detailed record

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