'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.

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.

Inequalities and Extremal Problems in Probability and Statistics: Selected Topics presents various kinds of useful inequalities that are applicable in many areas of mathematics, the sciences, and engineering. The book enables the reader to grasp the importance of inequalities and how they relate to probability and statistics. This will be an extremely useful book for researchers and graduate students in probability, statistics, and econometrics, as well as specialists working across sciences, engineering, financial mathematics, insurance, and mathematical modeling of large risks.