Coherent risk measures

The notes grew out of a course I taught at a Cattedra Galileiana at the Scuola Normale Superiore di Pisa, March 2000. The aim of these lectures was to show that it is possible to translate problems from Risk Management into mathematics and back. Part of the course was devoted to an analysis of Value at Risk and its relation to quantiles. We concentrate on the mathematics behind the concept of coherent risk measures.