Providing comprehensive yet accessible coverage, this is the first graduate-level textbook dedicated to the mathematical theory of risk measures. It explains how economic and financial principles result in a profound mathematical theory that allows us to quantify risk in monetary terms, giving rise to risk measures. Each chapter is designed to match the length of one or two lectures, covering the core theory in a self-contained manner, with exercises included in every chapter. Additional material sections then provide further background and insights for those looking to delve deeper. This two-layer modular design makes the book suitable as the basis for diverse lecture courses of varying length and level, and a valuable resource for researchers.

‘This book presents the one period theory of risk measurement or monetary utility functions. Since their introduction in the nineties, the theory and its applications have undergone a lot of changes. It is the right time to compile the advances in a new book. To benefit fully, the reader should follow the advice of Paul Halmos: to learn mathematics you must do mathematics and therefore should certainly solve the numerous exercises that accompany every chapter. Some of them are trivial, but not easy; some are intermediate. The last chapter puts emphasis on multivalued risk measurement which is a new development. The reader (solving the exercises) will learn a lot when studying this book.’

Freddy Delbaen - ETH Zurich