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Lundberg bounds on the tails of compound distributions

Part of: Special processes

Published online by Cambridge University Press:  14 July 2016

Gordon E. Willmot  and
Xiaodong Lin
Gordon E. Willmot
Affiliation:
University of Waterloo
Xiaodong Lin*
Affiliation:
University of Waterloo
*
∗ Postal address: Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, Ontario, Canada, N2L 3G1.
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Abstract

Exponential bounds are derived for the tail probabilities of various compound distributions, generalizing the classical Lundberg inequality of insurance risk theory. Failure rate properties of the compounding distribution including log-convexity and log-concavity are considered in some detail. Mixed Poisson compounding distributions are also considered. A ruin theoretic generalization of the Lundberg inequality is obtained in the case where the number of claims process is a mixed Poisson process. An application to the M/G/1 queue length distribution is given.

Keywords

INSURANCE RISKCOMPLETELY MONOTONELOG-CONVEXLOG-CONCAVECOMPOUND GEOMETRICMIXED POISSONFAILURE RATEMEAN RESIDUAL LIFETIMEM/G/1 QUEUE

MSC classification

Primary: 60K25: Queueing theory
Type
Research Papers
Information
Journal of Applied Probability , Volume 31 , Issue 3 , September 1994 , pp. 743 - 756
Copyright
Copyright © Applied Probability Trust 1994 

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