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Upper bounds on the expected time to ruin and on the expected recovery time

Part of: Mathematical economics Special processes

Published online by Cambridge University Press:  01 July 2016

Esther Frostig
Esther Frostig*
Affiliation:
University of Haifa
*
∗ Postal address: Department of Statistics, University of Haifa, Haifa 31905, Israel. Email address: [email protected]
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Abstract

It is shown that the time to ruin and the recovery time in a risk process have the same distribution as the busy period in a certain queueing system. Similarly, the deficit at the time of ruin is distributed as the idle period in a single-server queueing system. These duality results are exploited to derive upper bounds for the expected time to ruin and the expected recovery time as defined by Egídio dos Reis (2000). When the claim size is generally distributed, Lorden's inequality is applied to derive the bounds. When the claim-size distribution is of phase type, tighter upper bounds are derived.

Keywords

Risk processtime to ruinduration of negative surplusM/G/1 queueing systemG/M/1 queueing systemPH/PH/1 queueing systembusy periodidle periodLorden's inequalityphase-type distribution

MSC classification

Primary: 91B30: Risk theory, insurance
Secondary: 60K25: Queueing theory
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 36 , Issue 2 , June 2004 , pp. 377 - 397
Copyright
Copyright © Applied Probability Trust 2004 

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