Asymptotic Theory for a Risk Process with a High Dividend Barrier

Johan Irbäck

Scandinavian Actuarial Journal, 2003, vol. 2003, issue 2, 97-118

Abstract: The only way to avoid ruin in the classical model of the collective risk theory is that the surplus increases to infinity. We consider a modified model with a dividend barrier that prevents this behavior. It is shown that there is a simple approximation formula for the time of ruin when the level of the dividend barrier is high and the Cramér-Lundberg condition is satisfied. A numerical example is presented in the case when the claims are exponentially distributed. The relation to queuing theory is used to derive the proportion of time the surplus is below some given level.

Date: 2003
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DOI: 10.1080/03461230110106345

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