Large Claims in Insurance Mathematics

I take great pleasure m addressing this audience. As you might know I'm a mathematician with a deep interest in insurance mathematics. As such, it is my sincere opinion that the gap between practicing actuaries and theoretical researchers can be made substantially smaller. If my contribution can help in bridging the gap, I will feel fully compensated for the effort it took to prepare this lecture and the results contained therein. The simple fact that we meet on the occasion of the sixteenth ASTIN Colloquium gives me a challenging opportunity to help in creating a platform on which both theoreticians and practitioners can meet. The subject of my lecture stems from a long interest in large claims: What are they? Are they really dangerous 9 Is there a way to get them under control? Can one recognize them in practical situations?