On the analysis of a multi-threshold Markovian risk model |
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Authors: | Andrei Badescu Steve Drekic |
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Institution: | 1. Department of Statistics , University of Toronto , Toronto, Ontario, M5S 363, Canada;2. Department of Statistics and Actuarial Science , University of Waterloo , Waterloo, Ontario, N2L 361, Canada |
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Abstract: | We consider a class of Markovian risk models perturbed by a multiple threshold dividend strategy in which the insurer collects premiums at rate c i whenever the surplus level resides in the i-th surplus layer, i=1, 2, …,n+1 where n<∞. We derive the Laplace-Stieltjes transform (LST) of the distribution of the time to ruin as well as the discounted joint density of the surplus prior to ruin and the deficit at ruin. By interpreting that the insurer, whose gross premium rate is c, pays dividends continuously at rate d i =c?c i whenever the surplus level resides in the i-th surplus layer, we also derive the expected discounted value of total dividend payments made prior to ruin. Our results are obtained via a recursive approach which makes use of an existing connection, linking 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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