High Risk Scenarios and Extremes

A geometric approach

  • Guus Balkema

    University of Amsterdam, The Netherlands
  • Paul Embrechts

    ETH Zurich, Switzerland
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Frontmatter, Foreword, AcknowledgementsDownload pp. i–viii
ContentsDownload pp. ix–xiii
IntroductionDownload pp. 1–11
PreviewDownload pp. 13–39
IPoint Processesp. 41
1An intuitive approachpp. 41–47
2Poisson point processespp. 48–63
3The distributionpp. 63–69
4Convergencepp. 69–81
5Converging sample cloudspp. 81–99
IIMaximap. 100
6The univariate theory: maxima and exceedancespp. 100–110
7Componentwise maximapp. 110–122
IIIHigh Risk Limit Lawsp. 123
8High risk scenariospp. 123–135
9The Gauss-exponential domain, rotund setspp. 135–147
10The Gauss-exponential domain, unimodal distributionspp. 147–156
11Flat functions and flat measurespp. 156–169
12Heavy tails and bounded vectorspp. 170–176
13The multivariate GPDspp. 176–181
IVThresholdsp. 182
14Exceedances over horizontal thresholdspp. 183–211
15Horizontal thresholds – examplespp. 211–230
16Heavy tails and elliptic thresholdspp. 230–263
17Heavy tails – examplespp. 263–295
18Regular variation and excess measurespp. 295–347
Open problemsp. 348
19The stochastic modelpp. 349–356
20The statistical analysispp. 356–360
Bibliographypp. 361–368
Indexpp. 369–375