EAA Series

Gerber–Shiu Risk Theory

Authors: Kyprianou, Andreas E.

  • 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
see more benefits

Buy this book

eBook $39.99
price for USA (gross)
  • ISBN 978-3-319-02303-8
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $49.99
price for USA
  • ISBN 978-3-319-02302-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
About this Textbook

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)


Table of contents (9 chapters)

  • Introduction

    Kyprianou, Andreas E.

    Pages 1-8

  • The Wald Martingale and the Maximum

    Kyprianou, Andreas E.

    Pages 9-15

  • The Kella–Whitt Martingale and the Minimum

    Kyprianou, Andreas E.

    Pages 17-26

  • Scale Functions and Ruin Probabilities

    Kyprianou, Andreas E.

    Pages 27-35

  • The Gerber–Shiu Measure

    Kyprianou, Andreas E.

    Pages 37-43

Buy this book

eBook $39.99
price for USA (gross)
  • ISBN 978-3-319-02303-8
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $49.99
price for USA
  • ISBN 978-3-319-02302-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
Loading...

Recommended for you

Loading...

Bibliographic Information

Bibliographic Information
Book Title
Gerber–Shiu Risk Theory
Authors
Series Title
EAA Series
Copyright
2013
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-02303-8
DOI
10.1007/978-3-319-02303-8
Softcover ISBN
978-3-319-02302-1
Series ISSN
1869-6929
Edition Number
1
Number of Pages
VIII, 93
Number of Illustrations and Tables
4 b/w illustrations, 3 illustrations in colour
Topics