Overview
- Provides a comprehensive treatment of Sparre Andersen risk processes arising from models in actuarial science
- Offers an in-depth analysis of standard models, with a rigorous mathematical presentation
- Presents ideas and techniques that may be adapted to other models as appropriate
- Explores dependence features, such as claim size and interclaim time
- Includes supplementary material: sn.pub/extras
Part of the book series: Springer Actuarial (SPACT)
Access this book
Tax calculation will be finalised at checkout
Other ways to access
Table of contents (8 chapters)
-
Front Matter
-
Back Matter
Keywords
- MSC (2010): 60-02, 60G50, 60K10, 62P05
- dependent Sparre Andersen risk model
- classical compound poisson risk model
- classical Poisson risk model derivation
- classical Poisson risk model analysis
- Gerber Shiu function
- ruin probability
- deficit at ruin
- time of ruin
- mixed Erlang distribution
- defective renewal equation
- renewal risk process
- Laplace transform
- Dickson Hipp operator
- delayed renewal risk model
- discrete renewal risk model
About this book
This carefully written monograph covers the Sparre Andersen process in an actuarial context using the renewal process as the model for claim counts.
A unified reference on Sparre Andersen (renewal risk) processes is included, often missing from existing literature. The authors explore recent results and analyse various risk theoretic quantities associated with the event of ruin, including the time of ruin and the deficit of ruin. Particular attention is given to the explicit identification of defective renewal equation components, which are needed to analyse various risk theoretic quantities and are also relevant in other subject areas of applied probability such as dams and storage processes, as well as queuing theory.
Aimed at researchers interested in risk/ruin theory and related areas, this work will also appeal to graduate students in classical and modern risk theory and Gerber-Shiu analysis.
Reviews
Authors and Affiliations
About the authors
Gordon E. Willmot is Munich Re Chair in Insurance and professor in the Department of Statistics and Actuarial Science at the University of Waterloo, Canada. His research interests are in stochastic modelling in insurance. Willmot has (co-)authored over one hundred research papers in leading actuarial and statistical journals. He is also co-author of Lundberg Approximations for Compound Distributions with Insurance Applications (Springer), Loss Models - From Data to Decisions and Loss Models - Further Topics (Wiley), and Insurance Risk Models (Society of Actuaries). He is editor of Insurance: Mathematics and Economics.
Jae-Kyung Woo is Associate Professor in the School of Risk and Actuarial Studies at the University of New South Wales, Sydney. She has worked at the University of Hong Kong and Columbia University prior to joining UNSW. Her research interests are focused on risk theory, reliability theory, aggregate claim analysis,and queueing theory. She has published about twenty papers dealing with the subject of the present monograph and related topics.
Bibliographic Information
Book Title: Surplus Analysis of Sparre Andersen Insurance Risk Processes
Authors: Gordon E. Willmot, Jae-Kyung Woo
Series Title: Springer Actuarial
DOI: https://doi.org/10.1007/978-3-319-71362-5
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing AG 2017
Hardcover ISBN: 978-3-319-71361-8Published: 08 January 2018
Softcover ISBN: 978-3-319-89066-1Published: 06 June 2019
eBook ISBN: 978-3-319-71362-5Published: 21 December 2017
Series ISSN: 2523-3262
Series E-ISSN: 2523-3270
Edition Number: 1
Number of Pages: VIII, 225
Number of Illustrations: 3 b/w illustrations