Background
Evaluating and managing risk is a very challenging task. Indeed there are many factors that contribute to the risk involved in any given action.

We all experience complexity in everyday life, where simple answers are hard to find and the consequences of our actions are difficult to predict. Modern science recognizes that problems involving the collective behavior of many interacting elements (such as humans, cells or information) are often “complex”. These systems typically display collective, organized behavior that cannot be predicted from usual study of their components in isolation. The resulting responses of complex systems are often counterintuitive. Their explanation requires the use of new tools and new paradigms which range from network theory to multi-scale analysis

We need tools that enable us to predict a given outcome, to evaluate its size, to understand how other related or unrelated quantities will simultaneously behave and finally to put all together in a simple form –a number– that can be used in practical cases….

Course Topic and Contents
- Probability theory;
- Fat tail, power law distributions;
- Central limit Theorem and extension to Levy stable distributions;
- Stable distributions;
- Infinitely divisible processes;
- Extreme value theory;
- Measuring the distribution tails;
- Stochastic processes;
- Power law jumps;
- Fractional calculus;
- Super- and Sub- diffusive evolution;
- Scaling relations;
- Uni- scaling and Multi- scaling processes;
- Autocorrelations;
- Cross- correlations and dependency;
- Network theory;
- Critical propagation in networks, epidemic spread and cascading evens;
- Information filtering.