Dynamic Models for Volatility and Heavy Tails, Harvey

Автор: Rachev, Svetlozar T. Kim, Young Shim Bianchi, Mich
Название: Financial models with levy processes and volatility clustering
ISBN: 0470482354 ISBN-13(EAN): 9780470482353
Издательство: Wiley
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Описание: * In this book, authors Rachev, Kim, Bianchi, and Fabozzi present readers with the notions of risk and their corresponding performance measures.

Автор: Buraczewski
Название: Stochastic Models with Power-Law Tails
ISBN: 3319296787 ISBN-13(EAN): 9783319296784
Издательство: Springer
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Описание: In this monograph the authors give a systematic approach to theprobabilistic properties of the fixed point equation X=AX+B. Aprobabilistic study of the stochastic recurrence equation X_t=A_tX_{t-1}+B_tfor real- and matrix-valued random variables A_t, where (A_t,B_t) constitute aniid sequence, is provided. The classical theory for these equations, includingthe existence and uniqueness of a stationary solution, the tail behavior withspecial emphasis on power law behavior, moments and support, is presented. Theauthors collect recent asymptotic results on extremes, point processes, partialsums (central limit theory with special emphasis on infinite variance stablelimit theory), large deviations, in the univariate and multivariate cases, andthey further touch on the related topics of smoothing transforms, regularlyvarying sequences and random iterative systems.The text gives an introduction to the Kesten-Goldie theory forstochastic recurrence equations of the type X_t=A_tX_{t-1}+B_t. It provides the classical results ofKesten, Goldie, Guivarc'h, and others, and gives an overview of recentresults on the topic. It presents the state-of-the-art results in the field ofaffine stochastic recurrence equations and shows relations with non-affinerecursions and multivariate regular variation.