On the compound Poisson risk model with dependence and a threshold dividend strategy

In this paper, we consider the compound Poisson risk model with a threshold dividend strategy and a dependence structure modeled by a Farlie-Gumbel-Morgenstern copula. The integro-differential equations satisfied by the Gerber-Shiu functions and the expected discounted dividend payments paid until ruin respectively are derived. Further, by deriving and solving the renewal equations satisfied by the Gerber-Shiu functions and the expected discounted dividend payments, we give the explicit formulas for them.