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Surplus Analysis of Sparre Andersen Insurance Risk Processes

  • Gordon E. Willmot
  • Jae-Kyung Woo

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

  • Gordon E. Willmot
    • 1
  • Jae-Kyung Woo
    • 2
  1. 1.Department of Statistics and Actuarial ScienceUniversity of WaterlooWaterlooCanada
  2. 2.School of Risk and Actuarial StudiesUniversity of New South WalesSydneyAustralia

Bibliographic information

  • 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
  • Print ISBN 978-3-319-71361-8
  • Online ISBN 978-3-319-71362-5
  • Series Print ISSN 2523-3262
  • Series Online ISSN 2523-3270
  • Buy this book on publisher's site