1.

Record Nr.

UNINA9910878974603321

Autore

Resnick Sidney

Titolo

The Art of Finding Hidden Risks : Hidden Regular Variation in the 21st Century / / by Sidney Resnick

Pubbl/distr/stampa

Cham : , : Springer Nature Switzerland : , : Imprint : Springer, , 2024

ISBN

9783031575990

9783031575983

Edizione

[1st ed. 2024.]

Descrizione fisica

1 online resource (272 pages)

Disciplina

519.535

Soggetti

Stochastic processes

Probabilities

Stochastic Processes

Applied Probability

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Nota di bibliografia

Includes bibliographical references and index.

Nota di contenuto

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.

Sommario/riassunto

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.