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Estimates for the Absolute Ruin Probability in the Compound Poisson Risk Model with Credit and Debit Interest

Part of: Limit theorems Special processes

Published online by Cambridge University Press:  14 July 2016

Jinxia Zhu  and
Hailiang Yang
Jinxia Zhu*
Affiliation:
The University of Hong Kong
Hailiang Yang*
Affiliation:
The University of Hong Kong
*
∗Current address: Australian School of Business, The University of New South Wales, Sydney, Australia. Email address: jinxia.zhu@unsw.edu.au
∗∗Postal address: Department of Statistics and Actuarial Science, The University of Hong Kong, Pokfulam Road, Hong Kong. Email address: hlyang@hkusua.hku.hk
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Abstract

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In this paper we consider a compound Poisson risk model where the insurer earns credit interest at a constant rate if the surplus is positive and pays out debit interest at another constant rate if the surplus is negative. Absolute ruin occurs at the moment when the surplus first drops below a critical value (a negative constant). We study the asymptotic properties of the absolute ruin probability of this model. First we investigate the asymptotic behavior of the absolute ruin probability when the claim size distribution is light tailed. Then we study the case where the common distribution of claim sizes are heavy tailed.

Keywords

Absolute ruin probabilitycredit and debit interest ratescompound Poisson modelheavy-tailed and light-tailed distributionsasymptotic results

MSC classification

Secondary: 60K10: Applications (reliability, demand theory, etc.) 60K20: Applications of Markov renewal processes (reliability, queueing networks, etc.) 60F99: None of the above, but in this section
Type
Research Article
Information
Journal of Applied Probability , Volume 45 , Issue 3 , September 2008 , pp. 818 - 830
Copyright
Copyright © Applied Probability Trust 2008 

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