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On the expected time to ruin and the expected dividends when dividends are paid while the surplus is above a constant barrier

Part of: Mathematical economics Special processes Stochastic processes

Published online by Cambridge University Press:  14 July 2016

Esther Frostig
Esther Frostig*
Affiliation:
University of Haifa
*
∗Postal address: Department of Statistics, University of Haifa, Haifa, 31905, Israel. Email address: frostig@stat.haifa.ac.il
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Abstract

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We study the expected time to ruin in a risk process in which dividends are paid when the surplus is above the barrier. We consider the case in which the dividend rate is smaller than the premium rate. We obtain results for the classical compound Poisson risk process with phase-type claim size. When the ruin probability is 1, we derive the expected time to ruin and the expected dividends paid. When the ruin probability is less than 1, these quantities are derived conditioning on the event that ruin occurs.

Keywords

Risk processruin probabilityphase-type distributionstopping timemartingaleM/G/1 queuebusy periodidle periodPH/M/1 queuefluid modelchange of measureLundberg coefficient

MSC classification

Primary: 91B30: Risk theory, insurance
Secondary: 60K25: Queueing theory 60G40: Stopping times; optimal stopping problems; gambling theory 60G44: Martingales with continuous parameter
Type
Research Papers
Information
Journal of Applied Probability , Volume 42 , Issue 3 , September 2005 , pp. 595 - 607
Copyright
© Applied Probability Trust 2005 

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