Quantifying extreme risks

Understanding and managing risks caused by extreme events is one of the most demanding problems of our society. We consider this topic from a statistical point of view and present some of the probabilistic and statistical theory, which was developed to model and quantify extreme events. By the very nature of an extreme event there will never be enough data to predict a future risk in the classical statistical sense. However, a rather clever probabilistic theory provides us with model classes relevant for the assessment of extreme events. Moreover, specific statistical methods allow for the prediction of rare events, even outside the range of previous observations. We will present the basic theory and relevant examples from climatology (climate change), insurance (return periods of large claims) and finance (portfolio losses and Value-At-Risk estimation).