Portfolio analysis and optimization, together with the associated risk assessment and management, require knowledge of the likely distributions of returns at different time scales and insights into the nature and properties of dependences between the different assets. This book offers an original and thorough treatment of these two domains, focusing mainly on the concepts and tools that remain valid for large and extreme price moves. Strong emphasis is placed on the theory of copulas and their empirical testing and calibration, because they offer intrinsic and complete measures of dependences. Extreme Financial Risks will be useful to: students looking for a general and in-depth introduction to the field; financial engineers, economists, econometricians, actuarial professionals; researchers and mathematicians looking for a synoptic view comparing the pros and cons of different modelling strategies; and quantitative practitioners for the insights offered on the subtleties and the many dimensional components of both risk and dependence. In toto, the content of this book will also be useful to a broader scientific community interested in quantifying the complexity of many natural and artificial processes in which a growing emphasis is on the role and importance of extreme phenomena.