Implications of Heavy-Tailedness

  • Marat Ibragimov
  • Rustam Ibragimov
  • Johan Walden
Part of the Lecture Notes in Statistics book series (LNS, volume 214)


This chapter demonstrates how majorization theory provides a powerful tool for the study of robustness of many important models in economics, finance, econometrics, statistics, risk management, and insurance to heavy-tailedness assumptions. The majorization relation is a formalization of the concept of diversity in the components of vectors. Over the past decades, majorization theory, which focuses on the study of this relation and functions that preserve it, has found applications in disciplines ranging from statistics, probability theory, and economics to mathematical genetics, linear algebra, and geometry (see Marshall et al. 2011, and the references therein).


Systemic Risk Reservation Price Credit Default Swap Capital Requirement Tail Index 
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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Marat Ibragimov
    • 1
  • Rustam Ibragimov
    • 2
  • Johan Walden
    • 3
  1. 1.Institute of Economics and FinanceKazan Federal UniversityKazanRussia
  2. 2.Imperial College Business SchoolLondonUK
  3. 3.University of California at Berkeley Walter A. Haas School of BusinessBerkeleyUSA

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