Modelling of Low Probability High Impact Events

In many real world phenomena the need for modelling of losses caused by an underlying process that generates both large number of occurrences with minor losses and occurrences with severe impact exists. Prominent examples are natural disasters (earthquakes, hurricanes, tornadoes etc.), operational losses in highly regulated institutions or claims generated by an insurance policy. In each case, the aggregated loss distribution can be modelled with a so called compound model that is a combination of two separate distributions describing the number of events and their severities. In the first part of this book in-depth description of the compound model is provided. The formal discussion is then followed by a case study, in which the previously elaborated theory is applied to model yearly losses incurred due to tornadoes in the United States.