Chapter 5 of Quantitative Enterprise Risk Management

By Mary R. Hardy and David Saunders · Society of Actuaries · 2022 · ASTAM-22-23

Study guide: Exam ASTAM

Extreme Value Theory, the fifth chapter of Quantitative Enterprise Risk Management by Mary R. Hardy and David Saunders, reprinted by the Society of Actuaries as a study note for the Advanced Short-Term Actuarial Mathematics exam with the permission of Cambridge University Press. The chapter presents key results from extreme value theory (EVT) and shows how EVT can supplement traditional statistical analysis when the concern is the impact of very rare, very large losses.

On the syllabus

• Exam ASTAM — ASTAM-22-23: Chapter 5 of Quantitative Enterprise Risk Management, 2022, by Hardy, M.R. and Saunders, D., Cambridge University Press, ISBN 978-1009098465.

5 Extreme Value Theory

• 5.1 Summary
• 5.2 Introduction
• 5.3 Distributions of Block Maxima
  • 5.3.1 Block Maxima and the Maximum Domain of Attraction
  • 5.3.2 The Generalized Extreme Value Distribution
  • 5.3.3 Notes on the Generalized Extreme Value
  • 5.3.4 Estimating the GEV Parameters
• 5.4 Distribution of Excess Losses Over a Threshold
  • 5.4.1 The Excess Loss Random Variable
  • 5.4.2 The Generalized Pareto Distribution (GPD)
  • 5.4.3 Risk Measures for the GPD
  • 5.4.4 The Hill Estimator
• 5.5 Example: US Hurricane Losses, 1940–2012
• 5.6 Notes and Further Reading
• 5.7 Exercises

Sources

• ASTAM-22-23: Chapter 5 of Quantitative Enterprise Risk Management (SOA) — the document: title page (Hardy and Saunders, © 2022, reprinted with permission of Cambridge University Press), and every section and subsection heading of the chapter and the opening of its summary
• SOA Exam ASTAM syllabus, Fall 2026 — the citation and the book's ISBN as the syllabus prints it