Modelling Extremal Events

for Insurance and Finance

  • Paul Embrechts
  • Claudia Klüppelberg
  • Thomas Mikosch

Part of the Applications of Mathematics book series (SMAP, volume 33)

Table of contents

  1. Front Matter
    Pages I-XV
  2. Paul Emberchts, Claudia Klüppelberg, Thomas Mikosch
    Pages 1-19
  3. Paul Emberchts, Claudia Klüppelberg, Thomas Mikosch
    Pages 21-57
  4. Paul Emberchts, Claudia Klüppelberg, Thomas Mikosch
    Pages 59-111
  5. Paul Emberchts, Claudia Klüppelberg, Thomas Mikosch
    Pages 113-179
  6. Paul Emberchts, Claudia Klüppelberg, Thomas Mikosch
    Pages 181-218
  7. Paul Emberchts, Claudia Klüppelberg, Thomas Mikosch
    Pages 219-282
  8. Paul Emberchts, Claudia Klüppelberg, Thomas Mikosch
    Pages 283-370
  9. Paul Emberchts, Claudia Klüppelberg, Thomas Mikosch
    Pages 371-412
  10. Paul Emberchts, Claudia Klüppelberg, Thomas Mikosch
    Pages 413-550
  11. Back Matter
    Pages 551-648

About this book

Introduction

Both in insurance and in finance applications, questions involving extremal events (such as large insurance claims, large fluctuations, in financial data, stock-market shocks, risk management, ...) play an increasingly important role. This much awaited book presents a comprehensive development of extreme value methodology for random walk models, time series, certain types of continuous-time stochastic processes and compound Poisson processes, all models which standardly occur in applications in insurance mathematics and mathematical finance. Both probabilistic and statistical methods are discussed in detail, with such topics as ruin theory for large claim models, fluctuation theory of sums and extremes of iid sequences, extremes in time series models, point process methods, statistical estimation of tail probabilities. Besides summarising and bringing together known results, the book also features topics that appear for the first time in textbook form, including the theory of subexponential distributions and the spectral theory of heavy-tailed time series. A typical chapter will introduce the new methodology in a rather intuitive (tough always mathematically correct) way, stressing the understanding of new techniques rather than following the usual "theorem-proof" format. Many examples, mainly from applications in insurance and finance, help to convey the usefulness of the new material. A final chapter on more extensive applications and/or related fields broadens the scope further. The book can serve either as a text for a graduate course on stochastics, insurance or mathematical finance, or as a basic reference source. Its reference quality is enhanced by a very extensive bibliography, annotated by various comments sections making the book broadly and easily accessible.

Keywords

Analysis Statistical Methods extreme value theory insurance risk mathematical finance modeling sets tail estimation time series analysis

Authors and affiliations

  • Paul Embrechts
    • 1
  • Claudia Klüppelberg
    • 2
  • Thomas Mikosch
    • 3
  1. 1.Department of MathematicsETH ZurichZurichSwitzerland
  2. 2.Center for Mathematical SciencesMunich University of TechnologyGarchingGermany
  3. 3.Laboratory of Actuarial MathematicsUniversity of CopenhagenCopenhagenDenmark

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-33483-2
  • Copyright Information Springer-Verlag Berlin Heidelberg 1997
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-08242-9
  • Online ISBN 978-3-642-33483-2
  • Series Print ISSN 0172-4568
  • Series Online ISSN 2197-439X
  • About this book