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© 2017

Surplus Analysis of Sparre Andersen Insurance Risk Processes

Book

Part of the Springer Actuarial book series (SPACT)

Table of contents

  1. Front Matter
    Pages i-viii
  2. Gordon E. Willmot, Jae-Kyung Woo
    Pages 1-10
  3. Gordon E. Willmot, Jae-Kyung Woo
    Pages 11-43
  4. Gordon E. Willmot, Jae-Kyung Woo
    Pages 45-59
  5. Gordon E. Willmot, Jae-Kyung Woo
    Pages 61-78
  6. Gordon E. Willmot, Jae-Kyung Woo
    Pages 79-126
  7. Gordon E. Willmot, Jae-Kyung Woo
    Pages 127-149
  8. Gordon E. Willmot, Jae-Kyung Woo
    Pages 151-177
  9. Gordon E. Willmot, Jae-Kyung Woo
    Pages 179-215
  10. Back Matter
    Pages 217-225

About this book

Introduction

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.

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

Authors and affiliations

  1. 1.Department of Statistics and Actuarial ScienceUniversity of WaterlooWaterlooCanada
  2. 2.School of Risk and Actuarial StudiesUniversity of New South WalesSydneyAustralia

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
  • Series Abbreviated Title Springer Actuarial
  • DOI https://doi.org/10.1007/978-3-319-71362-5
  • Copyright Information Springer International Publishing AG 2017
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Hardcover ISBN 978-3-319-71361-8
  • Softcover ISBN 978-3-319-89066-1
  • eBook ISBN 978-3-319-71362-5
  • Series ISSN 2523-3262
  • Series E-ISSN 2523-3270
  • Edition Number 1
  • Number of Pages VIII, 225
  • Number of Illustrations 3 b/w illustrations, 0 illustrations in colour
  • Topics Actuarial Sciences
    Statistical Theory and Methods
  • Buy this book on publisher's site
Industry Sectors
Finance, Business & Banking

Reviews

“The monograph is devoted to the surplus analysis of the Sparre-Andersen process using the renewal process as the model for claim counts. … This book is intended for researchers interested in ruin/risk theory, and will also be useful for graduate students specialized in classical and modern risk theory.” (Anatoliy Swishchuk, zbMATH 1391.91006, 2018)