Chapter 7. Extreme value theory: The study of jumbo losses

  1. Harry H. Panjer

Published Online: 6 MAR 2006

DOI: 10.1002/0470051310.ch7

Operational Risk: Modeling Analytics

Operational Risk: Modeling Analytics

How to Cite

Panjer, H. H. (2006) Extreme value theory: The study of jumbo losses, in Operational Risk: Modeling Analytics, John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/0470051310.ch7

Publication History

  1. Published Online: 6 MAR 2006
  2. Published Print: 25 AUG 2006

ISBN Information

Print ISBN: 9780471760894

Online ISBN: 9780470051313



  • high frequency low severity (HFLS);
  • low frequency high severity (LFHS);
  • Gumbel distribution;
  • Frechet distribution;
  • Fisher-Tippett theorem


This chapter contains sections titled:

  • Introduction

  • Extreme Value Distributions

  • Distribution of the Maximum

  • Stability of the Maximum of the Extreme Value Distribution

  • The Fisher-Tippett Theorem

  • Maximum Domain of Attraction

  • Generalized Pareto Distributions

  • The Frequency of Exceedences

  • Stability of Excesses of the Generalized Pareto

  • Mean Excess Function

  • Limiting Distributions of Excesses

  • TVaR for Extreme Value Distributions

  • Further Reading

  • Exercises