The scientific study of complex systems has transformed a wide range of disciplines in recent years, enabling researchers in both the natural and social sciences to model and predict phenomena as diverse as earthquakes, global warming, demographic patterns, financial crises, and the failure of...

In the real world, the variance of portfolio returns provides only a limited quantification of incurred risks, as the distributions of returns have “fat tails” and the dependence between assets are only imperfectly accounted for by the correlation matrix. Value‐at‐risk and other measures...

This paper offers a precise analytical characterization of the distribution of returns for a portfolio constituted of assets whose returns are described by an arbitrary joint multivariate distribution. In this goal, we introduce a non-linear transformation that maps the returns onto gaussian...