The compound Poisson risk model under a mixed dividend strategy

In this paper, we consider a compound Poisson model under a mixed dividend strategy. The mixed dividend strategy is a combination of threshold dividend strategy and periodic dividend strategy. Given a positive threshold level b > 0, whenever the surplus process attains the level b, dividends will be paid off continuously at a rate α > 0. Furthermore, given a sequence of dividend decision times {Zj}j=1∞, whenever the observed surplus level at Zj is larger than b, the excess value will also be paid off as dividend. We study the expected discounted dividend payments before ruin and the Gerber-Shiu expected discounted penalty function. Some numerical examples are also presented.