… to a loss larger than that of Y (ie, all components of the vector X in RN are always less than
or equal to those of the vector Y), the risk measure ρ(X) must be larger than or equal to ρ(Y) : …

… To cite this article: Y Malevergne and D Sornette 2003 Quantitative Finance 3 231 … To
make it clear, first consider the case where for large X and Y the distribution function F(x,y) …

… distinguishing distributions in their tails (Malevergne et al., 2005; Malevergne and Sornette,
2006). In a forthcoming paper, … The Wiener process with drift Y(t) given by (2.6) is solution to …

A large consensus now seems to take for granted that the distributions of empirical returns
of financial time series are regularly varying, with a tail exponent b close to 3. We develop a …

… 1 shows that the 95% confidence interval covers the empirical DF Fn(y) in the tail range, but
there are some other places along the distribution for which the empirical DF Fn(y) goes out …

Zipf's law states that the number of firms with size greater than S is inversely proportional to
S. Most explanations start with Gibrat's rule of proportional growth but require additional …

… Malevergne is with the Univ Lyon, UJM-Saint-Etienne, COACTIS, EA 4161, F-42023 Saint
… Yannick Malevergne received the Ph.D. degree in physics from the University of Nice, Nice, …

Imitative and contrarian behaviours are the two typical opposite attitudes of investors in stock
markets. We introduce a simple model to investigate their interplay in a stock market where …

The heavy-tailed distribution of firm sizes first discovered by Zipf (1949) is one of the best
established empirical facts in economics. We show that it has strong implications for asset …

Through simple analytical calculations and numerical simulations, we demonstrate the
generic existence of a self-organized macroscopic state in any large multivariate system …