Heavy-Tailed Distributions and Robustness in Economics and Finance

verfasst von: Marat Ibragimov, Rustam Ibragimov, Johan Walden

Verlag: Springer International Publishing

Buchreihe : Lecture Notes in Statistics

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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Über dieses Buch

This book focuses on general frameworks for modeling heavy-tailed distributions in economics, finance, econometrics, statistics, risk management and insurance. A central theme is that of (non-)robustness, i.e., the fact that the presence of heavy tails can either reinforce or reverse the implications of a number of models in these fields, depending on the degree of heavy-tailed ness. These results motivate the development and applications of robust inference approaches under heavy tails, heterogeneity and dependence in observations. Several recently developed robust inference approaches are discussed and illustrated, together with applications.

Inhaltsverzeichnis

Frontmatter

Chapter 1. Introduction

Abstract

The empirical and theoretical study of heavy-tailed distributions within economics and finance is by now a mature area of research, dating back more than 50 years. The first empirical study is usually attributed to Mandelbrot (1963), who noted that the changes of cotton prices seem to be well approximated by heavy-tailed so-called stable distributions. Loosely speaking, this means that rare events tend to happen much more often than they would if risk distributions had standard Gaussian (or other) thin tails. For example, the approximately 20 % drop of the stock market on the so-called Black Monday of October 19, 1987 would occur much less often than once in a billion years under standard assumptions of Gaussian distributions, and has been taken as evidence that stock market returns are heavy-tailed (see, for instance, the striking examples in Chap. 2 in Stock and Watson 2007 that illustrate inappropriateness of Gaussian distributions as models for financial returns based on their behavior during the Black Monday crisis).

Marat Ibragimov, Rustam Ibragimov, Johan Walden

Chapter 2. Implications of Heavy-Tailedness

Abstract

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).

Marat Ibragimov, Rustam Ibragimov, Johan Walden

Chapter 3. Inference and Empirical Examples

Abstract

Several approaches to the inference about the tail index ζ of heavy-tailed distributions are available in the literature (see, among others, the reviews in Beirlant et al. 2004; Embrechts et al. 1997). The two most commonly used ones are Hill’s estimator and the OLS approach using the log-log rank-size regression.

Marat Ibragimov, Rustam Ibragimov, Johan Walden

Backmatter

Titel: Heavy-Tailed Distributions and Robustness in Economics and Finance
verfasst von: Marat Ibragimov
Rustam Ibragimov
Johan Walden
Verlag: Springer International Publishing
Electronic ISBN: 978-3-319-16877-7
Print ISBN: 978-3-319-16876-0
DOI: https://doi.org/10.1007/978-3-319-16877-7