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An identity based on the generalised negative binomial distribution with applications in ruin theory

Published online by Cambridge University Press:  10 September 2018

David C. M. Dickson
David C. M. Dickson*
Affiliation:
Centre for Actuarial Studies, Department of Economics, University of Melbourne, Melbourne, Victoria 3010, Australia
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Abstract

In this study, we show how expressions for the probability of ultimate ruin can be obtained from the probability function of the time of ruin in a particular compound binomial risk model, and from the density of the time of ruin in a particular Sparre Andersen risk model. In each case evaluation of generalised binomial series is required, and the argument of each series has a common form. We evaluate these series by creating an identity based on the generalised negative binomial distribution. We also show how the same ideas apply to the probability function of the number of claims in a particular Sparre Andersen model.

Keywords

Generalised negative binomial distributionGeneralised binomial seriesRuin probabilityTime of ruinErlang distribution
Type
Paper
Information
Annals of Actuarial Science , Volume 13 , Issue 2 , September 2019 , pp. 308 - 319
Copyright
© Institute and Faculty of Actuaries 2018 

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References

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