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Analysis of a Dividend Barrier Strategy for a Class of Markovian Risk Models

By Andrei Badescu, Steve Drekic and David L


We consider a class of Markovian risk models in which the insurer collects premiums at rate c1 (c2) whenever the surplus level is below (above) a constant barrier level b. We derive the LaplaceStieltjes transform (LST) of the distribution of the time to ruin as well as the LST (with respect to time) of the joint distribution of the time to ruin, the surplus prior to ruin, and the deficit at ruin. By interpreting that the insurer pays dividends continuously at rate c1 − c2 whenever the surplus level is above b, we also derive the expected discounted value of total dividend payments made prior to ruin. Our results are obtained by making use of an existing connection which links an insurer’s surplus process to an embedded fluid flow process

Topics: Sparre Andersen risk model, phasetype distribution, Markovian arrival process, LaplaceStieltjes transform
Year: 2014
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