Access this book
Tax calculation will be finalised at checkout
Other ways to access
About this book
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.
Similar content being viewed by others
Keywords
Table of contents (11 chapters)
-
Front Matter
-
Back Matter
Authors and Affiliations
Accessibility Information
Accessibility information for this book is coming soon. We're working to make it available as quickly as possible. Thank you for your patience.
Bibliographic Information
Book Title: Lundberg Approximations for Compound Distributions with Insurance Applications
Authors: Gordon E. Willmot, X. Sheldon Lin
Series Title: Lecture Notes in Statistics
DOI: https://doi.org/10.1007/978-1-4613-0111-0
Publisher: Springer New York, NY
-
eBook Packages: Springer Book Archive
Copyright Information: Springer Science+Business Media New York 2001
Softcover ISBN: 978-0-387-95135-5Published: 23 October 2000
eBook ISBN: 978-1-4613-0111-0Published: 06 December 2012
Series ISSN: 0930-0325
Series E-ISSN: 2197-7186
Edition Number: 1
Number of Pages: X, 250
Topics: Probability Theory and Stochastic Processes, Statistics for Business, Management, Economics, Finance, Insurance, Quantitative Finance