What is your next big one? A earthquake? A flood? A financial crisis? And when is it going to take place? We all know that predicting these events is difficult. But is it really impossible? In other words, is there any chance of having at least some basic information (in probabilistic terms) about the next big one?

In science and life, it is often crucial to understand whether a quantity of interest will or will not reach a predetermined critical level some time in the near future. This analysis becomes essential when the studied phenomenon may have a strong impact on human life, as in the case of floods, epidemics and financial crises, i.e. when a critical level corresponds to some sort of catastrophe, and the possibility of giving an alarm in due time is invaluable.

An alarm system is a tool predicting the occurrence of a catastrophic event at a specified time in the future on the basis of the available information. The system is meant to activate when the probability of a catastrophe in a given time horizon overcomes a certain predetermined threshold. An alarm system is said optimal when, given the available data, it shows the highest probability of correct alarm among all systems, while trying to minimize the number of false alarms, whose social and economic costs may be severe.

The development of new reliable alarm systems has therefore a strong potential impact in all those fields of science (epidemiology, finance, hydrology, geology, etc.), in which the correct prediction of extreme events is important.

In this talk, I will review some interesting results of the existing literature and propose some new techniques. Some applications will also be discussed.