1 . 1 Contracting maps as a new quantification of departure from Gaussian

We introduce a faithful representation of the heavy tail multivariate distribution of asset returns, as parsimonous as the Gaussian framework. Using calculation techniques of functional integration and Feynman diagrams borrowed from particle physics, we characterize precisely, through its cumulants of high order, the distribution of wealth variations of a portfolio composed of an arbitrary mixture of assets. The portfolio which minimizes the variance, i.e. the relatively " small " risks, often increases larger risks as measured by higher normalized cumulants and by the Value-at-risk.