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Lundberg Approximations for Compund Distributions With Insurance Applications | 
| Authors: Gordon E. Willmot, X. Sheldon Lin
Publisher: Springer
Category: Book
List Price: $79.95
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New (5) Used (5) from $56.28
Sales Rank: 2663739
Media: Paperback
Edition: 1
Number Of Items: 1
Pages: 250
Shipping Weight (lbs): 0.8
Dimensions (in): 9.1 x 6.1 x 0.6
ISBN: 0387951350
Dewey Decimal Number: 368.01
EAN: 9780387951355
ASIN: 0387951350
Publication Date: October 23, 2000
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Condition: New book, ships out within 24 hours, 100% satisfaction guaranteed, may have slight shelf wear
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Product Description
This monograph discusses Lundberg approximations for compound distributions with special emphasis on applications in insurance risk modeling. These distributions are somewhat awkward from an analytic standpoint, but play a central role in insurance and other areas of applied probability modeling such as queueing theory. Consequently, the material is of interest to researchers and graduate students interested in these areas. The material is self-contained, but an introductory course in insurance risk theory is beneficial to prospective readers. Lundberg asymptotics and bounds have a long history in connection with ruin probabilities and waiting time distributions in queueing theory, and have more recently been extended to compound distributions. This connection has its roots in the compound geometric representation of the ruin probabilities and waiting time distributions. A systematic treatment of these approximations is provided, drawing heavily on monotonicity ideas from reliability theory. The results are then applied to the solution of defective renewal equations, analysis of the time and severity of insurance ruin, and renewal risk models, which may also be viewed in terms of the equilibrium waiting time distribution in the G/G/1 queue. Many known results are derived and extended so that much of the material has not appeared elsewhere in the literature. A unique feature involves the use of elementary analytic techniques which require only undergraduate mathematics as a prerequisite. New proofs of many results are given, and an extensive bibliography is provided. Gordon Willmot is Professor of Statistics and Actuarial Science at the University of Waterloo. His research interests are in insurance risk and queueing theory. He is an associate editor of the North American Actuarial Journal.
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