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Heavy Tails and Copulas cover

"Overall, the book is highly technical, including full mathematical proofs of the results stated. Potential readers are post-graduate students or researchers in Quantitative Risk Management willing to have a manual with the state-of-the-art on portfolio diversification and risk aggregation with heavy tails, including the fundamental theorems as well as collateral (but most useful) results on majorization and copula theory."

Quantitative Finance

This book offers a unified approach to the study of crises, large fluctuations, dependence and contagion effects in economics and finance. It covers important topics in statistical modeling and estimation, which combine the notions of copulas and heavy tails — two particularly valuable tools of today's research in economics, finance, econometrics and other fields — in order to provide a new way of thinking about such vital problems as diversification of risk and propagation of crises through financial markets due to contagion phenomena, among others. The aim is to arm today's economists with a toolbox suited for analyzing multivariate data with many outliers and with arbitrary dependence patterns. The methods and topics discussed and used in the book include, in particular, majorization theory, heavy-tailed distributions and copula functions — all applied to study robustness of economic, financial and statistical models, and estimation methods to heavy tails and dependence.

Sample Chapter(s)
Foreword (48 KB)
Chapter 1: Introduction and Overview (202 KB)


Contents:
  • Introduction and Overview
  • Portfolio Diversification under Independent Fat Tailed Risks
  • From Independence to Dependence via Copulas and U-statistics
  • Limits of Diversification under Fat Tails and Dependence
  • Robustness of Econometric Methods to Copula Misspecification and Heavy Tails
  • Copula Tests Using Information Matrix
  • Summary and Conclusion

Readership: Advanced students in economics, finance, financial econometrics; risk managers; actuaries; finance professionals; business analysts; banking regulators; and for those interested in the functioning of modern financial markets and statistical models of financial contagion.

Free Access
FRONT MATTER
  • Pages:i–xvii

https://doi.org/10.1142/9789814689809_fmatter

Free Access
Chapter 1: Introduction and Overview
  • Pages:1–17

https://doi.org/10.1142/9789814689809_0001

No Access
Chapter 2: Portfolio Diversification under Independent Fat Tailed Risks
  • Pages:19–45

https://doi.org/10.1142/9789814689809_0002

No Access
Chapter 3: From Independence to Dependence via Copulas and U-statistics
  • Pages:47–111

https://doi.org/10.1142/9789814689809_0003

No Access
Chapter 4: Limits of Diversification under Fat Tails and Dependence
  • Pages:113–170

https://doi.org/10.1142/9789814689809_0004

No Access
Chapter 5: Robustness of Econometric Methods to Copula Misspecification and Heavy Tails
  • Pages:171–228

https://doi.org/10.1142/9789814689809_0005

No Access
Chapter 6: Copula Tests Using Information Matrix
  • Pages:229–255

https://doi.org/10.1142/9789814689809_0006

No Access
Chapter 7: Summary and Conclusion
  • Pages:257–260

https://doi.org/10.1142/9789814689809_0007

Free Access
BACK MATTER
  • Pages:261–284

https://doi.org/10.1142/9789814689809_bmatter

"Overall, the book is highly technical, including full mathematical proofs of the results stated. Potential readers are post-graduate students or researchers in Quantitative Risk Management willing to have a manual with the state-of-the-art on portfolio diversification and risk aggregation with heavy tails, including the fundamental theorems as well as collateral (but most useful) results on majorization and copula theory."

Quantitative Finance

"This is an excellent work, useful to both academics and practitioners, which contains two main novelties. First, it focuses on the ‘joint’ study of the concepts of heavy tails and copulas, unlike other books that consider only one of the two topics. Second, while giving a rigorous statistical and mathematical treatment, it frames the subjects in an economic and financial setup, where they are most relevant for applications. In my opinion, these contributions fill a gap in the current literature on quantitative methods in finance and economics. The combination of mathematical rigor and economic intuition makes the book a valuable tool for scholars with different backgrounds. Mathematicians and statisticians should be able to understand how familiar tools can boost the progress of knowledge in other sciences; economists find here the statistical techniques needed for incorporating outliners and complex dependence structures into their theoretical models."

Mathematical Review Clippings

Rustam Ibragimov is a Professor of Finance and Econometrics at the Imperial College Business School. Rustam received his PhD in Economics from Yale University in 2005. He also holds a PhD degree in Mathematics from the Uzbek Academy of Sciences. Following his graduation from Yale and prior to joining Imperial College, Rustam was an Assistant Professor (2005–2009) and then an Associate Professor (2009–2012) at Harvard's Economics Department. Over his academic career, he also held visiting positions at the Judge Business School at Cambridge, the Nuffield College at Oxford, the Department of Statistics at Columbia University, Innopolis University, Kazan (Volga Region) Federal University and other research and education centers in the former USSR. Rustam's works have appeared in leading journals in finance, economics, econometrics, statistics and probability such as the Journal of Financial Economics, Econometric Theory, Journal of Business and Economic Statistics and Annals of Probability. He serves as an Associate Editor for Econometric Theory and the Journal of Banking and Finance.


Artem Prokhorov is an Associate Professor at the University of Sydney Business School and an Adjunct Professor at St. Petersburg State University. Artem received his PhD in Economics from Michigan State University in 2006 and before joining the University of Sydney had worked as an Assistant Professor (2006–2011) and Associate Professor with tenure (2011–2013) at the Economics Department of Concordia University in Montreal, Canada, as well as a Research Associate at a German investment bank. Artem has published in leading scholarly journals in the field of econometrics such as the Journal of Econometrics and has been awarded multiple competitive research grants from such national agencies as the Social Sciences and Humanities Research Council of Canada (SSHRC) and the Research Fund of Quebec (FQRSC). He is a regular presenter at international conferences and invited seminars in econometrics and is often asked to serve as an expert witness in consultancy projects in his field. He has held a number of visiting professorial appointments at universities around the world, including Harvard University and the University of New South Wales, and is often invited to serve on scientific committees of international conferences. He is a Co-Editor of The St. Petersburg University Journal of Economic Studies, and an Associate Editor of Econometrics and Statistics (EcoSta) and the Rutgers Business Review.