On extreme value theory. Or: how to learn from almost disastrous events


Everybody has a personal bank account. Every month the salary is added to the balance. Now suppose that you are a big spender and you spend most of the money every month. It would be unpleasant if the balance would go down to zero during the month but this has never happened. You could be afraid of this event to happen and you would like to know the probability that in fact the balance would be depleted during a month. This is a difficult statistical problem since you want to estimate the probability of an event that has never happened and this seems impossible. Other similar examples are: Banks and insurance companies want to (have to) assess the probability that they go bankrupt in some given period of time. The regulator forces them to do so. A communication tower is much affected by wind storms, but the tower has never collapsed. Since much depends on this tower, one needs to know the probability of collapse. Problems of this kind can be attacked using a special branch of the area of mathematical statistics called extreme value theory. The theory has been developed over the last 70 years by scientists mainly from Europe and notably by Professor Tiago de Oliveira from this university. We are now able to provide a reliable answer to the mentioned questions. I want to explain some ideas and results of extreme value theory, in particular what is needed to answer the stated problems.