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Lundberg Approximations for Compound Distributions with Insurance Applications

  • Gordon E. Willmot
  • X. Sheldon Lin

Part of the Lecture Notes in Statistics book series (LNS, volume 156)

Table of contents

  1. Front Matter
    Pages i-x
  2. Gordon E. Willmot, X. Sheldon Lin
    Pages 1-5
  3. Gordon E. Willmot, X. Sheldon Lin
    Pages 7-36
  4. Gordon E. Willmot, X. Sheldon Lin
    Pages 37-49
  5. Gordon E. Willmot, X. Sheldon Lin
    Pages 51-80
  6. Gordon E. Willmot, X. Sheldon Lin
    Pages 81-91
  7. Gordon E. Willmot, X. Sheldon Lin
    Pages 93-105
  8. Gordon E. Willmot, X. Sheldon Lin
    Pages 107-140
  9. Gordon E. Willmot, X. Sheldon Lin
    Pages 141-149
  10. Gordon E. Willmot, X. Sheldon Lin
    Pages 151-181
  11. Gordon E. Willmot, X. Sheldon Lin
    Pages 183-208
  12. Gordon E. Willmot, X. Sheldon Lin
    Pages 209-234
  13. Back Matter
    Pages 235-252

About this book

Introduction

These notes represent our summary of much of the recent research that has been done in recent years on approximations and bounds that have been developed for compound distributions and related quantities which are of interest in insurance and other areas of application in applied probability. The basic technique employed in the derivation of many bounds is induc­ tive, an approach that is motivated by arguments used by Sparre-Andersen (1957) in connection with a renewal risk model in insurance. This technique is both simple and powerful, and yields quite general results. The bounds themselves are motivated by the classical Lundberg exponential bounds which apply to ruin probabilities, and the connection to compound dis­ tributions is through the interpretation of the ruin probability as the tail probability of a compound geometric distribution. The initial exponential bounds were given in Willmot and Lin (1994), followed by the nonexpo­ nential generalization in Willmot (1994). Other related work on approximations for compound distributions and applications to various problems in insurance in particular and applied probability in general is also discussed in subsequent chapters. The results obtained or the arguments employed in these situations are similar to those for the compound distributions, and thus we felt it useful to include them in the notes. In many cases we have included exact results, since these are useful in conjunction with the bounds and approximations developed.

Keywords

Binomial distribution G/G/1 queue Martingale Poisson distribution binomial modeling queueing theory statistics

Authors and affiliations

  • Gordon E. Willmot
    • 1
  • X. Sheldon Lin
    • 2
  1. 1.Department of Statistics and Actuarial ScienceUniversity of WaterlooWaterlooCanada
  2. 2.Department of Statistics and Actuarial ScienceUniversity of IowaIowa CityUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4613-0111-0
  • Copyright Information Springer-Verlag New York, Inc. 2001
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-0-387-95135-5
  • Online ISBN 978-1-4613-0111-0
  • Series Print ISSN 0930-0325
  • Buy this book on publisher's site