Risk Measures
An Introduction to the Mathematical Theory
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Product details:
- Publisher Cambridge University Press
- Date of Publication 19 February 2026
- ISBN 9781009710930
- Binding Paperback
- No. of pages208 pages
- Size 229x152x11 mm
- Weight 309 g
- Language English 689
Categories
Short description:
This is the first graduate-level textbook dedicated to the mathematical theory of risk measures, with an emphasis on duality results.
MoreLong description:
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
Table of Contents:
Introduction; Acknowledgements; 1. Gains, quantiles and Value-at-Risk; 2. Monetary property and acceptance sets; 3. Diversification, convexity and coherence; 4. Average-Value-at-Risk; 5. Dual representation of convex and coherent risk measures; 6. Representation theorems for risk measures on $L^p$-spaces; 7. Constructions of risk measures; 8. Law-determined risk measures; 9. Law-determined risk measures on $L^p$-spaces; 10. Comonotonicity and Choquet integrals; 11. Coherent comonotonic additive risk measures; 12. Multivariate risk measures; List of representations of coherent risk measures; List of important law-determined risk measures; References; Index.
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