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Lecture Notes in Statistics

Lundberg Approximations for Compound Distributions with Insurance Applications

Authors: Willmot, Gordon E., Lin, X. Sheldon

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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.

Table of contents (11 chapters)

Table of contents (11 chapters)

Buy this book

eBook $84.99
price for USA in USD (gross)
  • ISBN 978-1-4613-0111-0
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $109.99
price for USA in USD
  • ISBN 978-0-387-95135-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Lundberg Approximations for Compound Distributions with Insurance Applications
Authors
Series Title
Lecture Notes in Statistics
Series Volume
156
Copyright
2001
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-1-4613-0111-0
DOI
10.1007/978-1-4613-0111-0
Softcover ISBN
978-0-387-95135-5
Series ISSN
0930-0325
Edition Number
1
Number of Pages
X, 250
Topics