Analysis of a threshold dividend strategy for a MAP risk model |
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Authors: | Andrei Badescu Steve Drekic David Landriault |
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Institution: | 1. Department of Statistics , University of Toronto , Toronto, Ontario, M5S 3G3, Canada badescu@utstat.toronto.edu;3. Department of Statistics and Actuarial Science , University of Waterloo , Waterloo, Ontario, N2L 3G1, Canada |
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Abstract: | 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 threshold level b. We derive the Laplace-Stieltjes 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. |
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Keywords: | Sparre Andersen risk model Phase-type distribution Markovian arrival process Laplace-Stieltjes transform Correlated claims Surplus process Fluid queues |
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