02913nam 22005295 450 991087897460332120240802130232.09783031575990(electronic bk.)978303157598310.1007/978-3-031-57599-0(MiAaPQ)EBC31579291(Au-PeEL)EBL31579291(CKB)33623754600041(MiAaPQ)EBC31580404(Au-PeEL)EBL31580404(DE-He213)978-3-031-57599-0(EXLCZ)993362375460004120240802d2024 u| 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierThe Art of Finding Hidden Risks Hidden Regular Variation in the 21st Century /by Sidney Resnick1st ed. 2024.Cham :Springer Nature Switzerland :Imprint: Springer,2024.1 online resource (272 pages)Print version: Resnick, Sidney The Art of Finding Hidden Risks Cham : Springer,c2024 9783031575983 Includes bibliographical references and index.1 Foundation -- 2 Regular Variation -- 3 Hidden Regular Variation -- 4 Lévy Processes with Regularly Varying Distributions: Where Do the Jumps Go? -- 5 Statistics -- A A Crash Course on Regularly Varying Functions -- B Notation Summary -- References -- Index.This text gives a comprehensive, largely self-contained treatment of multivariate heavy tail analysis. Emphasizing regular variation of measures means theory can be presented systematically and without regard to dimension. Tools are developed that allow a flexible definition of "extreme" in higher dimensions and permit different heavy tails to coexist on the same state space leading to "hidden regular variation" and "steroidal regular variation". This emphasizes when estimating risks, it is important to choose the appropriate heavy tail. Theoretical foundations lead naturally to statistical techniques; examples are drawn from risk estimation, finance, climatology and network analysis. Treatments target a broad audience in insurance, finance, data analysis, network science and probability modeling. The prerequisites are modest knowledge of analysis and familiarity with the definition of a measure; regular variation of functions is reviewed but is not a focal point.Stochastic processesProbabilitiesStochastic ProcessesApplied ProbabilityStochastic processes.Probabilities.Stochastic Processes.Applied Probability.519.535Resnick Sidney103650MiAaPQMiAaPQMiAaPQ9910878974603321The Art of Finding Hidden Risks4206205UNINA