Skip to main content
  • Textbook
  • © 2013

Gerber–Shiu Risk Theory

  • Provides a self-contained and easy-to-read introduction to classical ruin theory
  • Includes recent developments in exotic ruin theory
  • Makes transparent the connection with the theory of spectrally negative Lévy processes
  • Includes supplementary material: sn.pub/extras

Part of the book series: EAA Series (EAAS)

Buy it now

Buying options

eBook USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 49.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

This is a preview of subscription content, log in via an institution to check for access.

Table of contents (9 chapters)

  1. Front Matter

    Pages I-VIII
  2. Introduction

    • Andreas E. Kyprianou
    Pages 1-8
  3. The Wald Martingale and the Maximum

    • Andreas E. Kyprianou
    Pages 9-15
  4. The Kella–Whitt Martingale and the Minimum

    • Andreas E. Kyprianou
    Pages 17-26
  5. Scale Functions and Ruin Probabilities

    • Andreas E. Kyprianou
    Pages 27-35
  6. The Gerber–Shiu Measure

    • Andreas E. Kyprianou
    Pages 37-43
  7. Reflection Strategies

    • Andreas E. Kyprianou
    Pages 45-55
  8. Perturbation-at-Maximum Strategies

    • Andreas E. Kyprianou
    Pages 57-65
  9. Refraction Strategies

    • Andreas E. Kyprianou
    Pages 67-78
  10. Concluding Discussion

    • Andreas E. Kyprianou
    Pages 79-89
  11. Back Matter

    Pages 91-93

About this book

Motivated by the many and long-standing contributions of H. Gerber and E. Shiu, this book gives a modern perspective on the problem of ruin for the classical Cramér–Lundberg model and the surplus of an insurance company. The book studies martingales and path decompositions, which are the main tools used in analysing the distribution of the time of ruin, the wealth prior to ruin and the deficit at ruin. Recent developments in exotic ruin theory are also considered. In particular, by making dividend or tax payments out of the surplus process, the effect on ruin is explored.

Gerber-Shiu Risk Theory can be used as lecture notes and is suitable for a graduate course. Each chapter corresponds to approximately two hours of lectures.

Reviews

From the book reviews:

“The book under review gives a modern perspective on the problems in ruin theory in the framework of the classical Cramér-Lundberg risk model. … This compact book combines rigorous mathematical treatments with discussions and contains a comprehensive bibliography on the related topics at the end of each chapter. … this book is well written and can serve as a major reference book for researchers and graduate students in ruin  theory and related areas.” (Shuanming Li, Mathematical Reviews, January, 2015)

Authors and Affiliations

  • Department of Mathematical Sciences, University of Bath, Bath, United Kingdom

    Andreas E. Kyprianou

Bibliographic Information

  • Book Title: Gerber–Shiu Risk Theory

  • Authors: Andreas E. Kyprianou

  • Series Title: EAA Series

  • DOI: https://doi.org/10.1007/978-3-319-02303-8

  • Publisher: Springer Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer International Publishing Switzerland 2013

  • Softcover ISBN: 978-3-319-02302-1Published: 16 October 2013

  • eBook ISBN: 978-3-319-02303-8Published: 02 October 2013

  • Series ISSN: 1869-6929

  • Series E-ISSN: 1869-6937

  • Edition Number: 1

  • Number of Pages: VIII, 93

  • Number of Illustrations: 4 b/w illustrations, 3 illustrations in colour

  • Topics: Probability Theory and Stochastic Processes, Actuarial Sciences

Buy it now

Buying options

eBook USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 49.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access