LEADER 02913nam 22005295 450 001 9910878974603321 005 20240802130232.0 010 $a9783031575990$b(electronic bk.) 010 $z9783031575983 024 7 $a10.1007/978-3-031-57599-0 035 $a(MiAaPQ)EBC31579291 035 $a(Au-PeEL)EBL31579291 035 $a(CKB)33623754600041 035 $a(MiAaPQ)EBC31580404 035 $a(Au-PeEL)EBL31580404 035 $a(DE-He213)978-3-031-57599-0 035 $a(EXLCZ)9933623754600041 100 $a20240802d2024 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 14$aThe Art of Finding Hidden Risks $eHidden Regular Variation in the 21st Century /$fby Sidney Resnick 205 $a1st ed. 2024. 210 1$aCham :$cSpringer Nature Switzerland :$cImprint: Springer,$d2024. 215 $a1 online resource (272 pages) 311 08$aPrint version: Resnick, Sidney The Art of Finding Hidden Risks Cham : Springer,c2024 9783031575983 320 $aIncludes bibliographical references and index. 327 $a1 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. 330 $aThis 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. 606 $aStochastic processes 606 $aProbabilities 606 $aStochastic Processes 606 $aApplied Probability 615 0$aStochastic processes. 615 0$aProbabilities. 615 14$aStochastic Processes. 615 24$aApplied Probability. 676 $a519.535 700 $aResnick$b Sidney$0103650 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 912 $a9910878974603321 996 $aThe Art of Finding Hidden Risks$94206205 997 $aUNINA