Here is an innovative treatment of three critical ingredients of successful portfolio analysis, risk assessment, risk management and portfolio optimization: (1) the characterization of processes underlying the time evolution of prices, (2) the corresponding distributions of returns at different time scales and (3) the nature and properties of dependences between the different assets. The text illustrates the strengths and limitations of stochastic models in management of extreme financial shocks, and studies the impact of conditioning on the size of large market moves on the measure of extreme dependences.