Risk Measures

This is the first graduate-level textbook dedicated to the mathematical theory of risk measures, with an emphasis on duality results.

This text provides a rigorous but accessible introduction to the mathematical theory of risk measures, an indispensable tool to quantitatively assess risks of financial transactions. Requiring only a standard background in probability, it can be used for self-study or form the basis of a graduate-level course.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.