Lundberg Approximations for Compound Distributions with Insurance Applications

Paperback | October 23, 2000

byGordon E. Willmot

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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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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, t...

Format:PaperbackDimensions:260 pages, 9.25 × 6.1 × 0 inPublished:October 23, 2000Publisher:Springer New YorkLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0387951350

ISBN - 13:9780387951355

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Table of Contents

Introduction.- Reliability Background.- Mixed Poisson Distributions.- Compound Distributions.- Bounds Based on Reliability Classifications.- Parametric Bounds.- Compound Geometric and Negative Binomial Distributions.- Tijms Approximations.- Defective Renewal Equations.- The Severity of Ruin.- Renewal Risk Processes.