The mathematical concept of measuring risk

Abstract

One of the key tasks in risk management is the quantification of risk implied by uncertain future scenarios which then has to be interpreted with respect to certain risk management decisions. Mathematically, the usual tool for doing so is a quantitative risk measure. The financial industry standard risk measure Value-At-Risk exhibits some serious deficiencies and a vital research activity has been ongoing to search for better alternatives. In this chapter we give an introduction to the general theory of monetary, convex, and coherent risk measures and present illustrating and motivating examples.