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In this paper, we consider the distribution of discounted dividend payments until ruin under a risk model with two independent classes of claims in which both of the two interclaim times have phasetype distributions and a constant dividend barrier. We obtain the integro-dierential equations with boundary conditions for the momentgenerating function of the sum of the discounted dividend payments until ruin. Explicit expressions for arbitrary moments of the discounted dividend payments aredoi:10.15672/hjms.20156510908 fatcat:hyherj5ypvfmxp52ko4bfwhmdq