Yannick Malevergne – författare

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; andquantitative 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.

Zipf’s law is one of the few quantitative reproducible regularities found in e- nomics. It states that, for most countries, the size distributions of cities and of rms (with additional examples found in many other scienti c elds) are power laws with a speci c exponent: the number of cities and rms with a size greater thanS is inversely proportional toS. Most explanations start with Gibrat’s law of proportional growth but need to incorporate additional constraints and ingredients introducing deviations from it. Here, we present a general theoretical derivation of Zipf’s law, providing a synthesis and extension of previous approaches. First, we show that combining Gibrat’s law at all rm levels with random processes of rm’s births and deaths yield Zipf’s law under a “balance” condition between a rm’s growth and death rate. We nd that Gibrat’s law of proportionate growth does not need to be strictly satis ed. As long as the volatility of rms’ sizes increase asy- totically proportionally to the size of the rm and that the instantaneous growth rate increases not faster than the volatility, the distribution of rm sizes follows Zipf’s law. This suggests that the occurrence of very large rms in the distri- tion of rm sizes described by Zipf’s law is more a consequence of random growth than systematic returns: in particular, for large rms, volatility must dominate over the instantaneous growth rate.