报告摘要：we consider the optimal dividend problem of the renewal risk model with phase-type distributed interclaim times and exponentially dis- tributed claim sizes. Assume that the phases of the interclaim times can be observed. We study the optimal dividend under the 2–order and the n–order (n ≥ 3)separately. In the case of 2–order phase-type distributed interclaim times, we show that the optimal dividend policy is the optimal phase-wise barrier strategy. As a byproduct, we find that in this case, the phase with higher barrier is the phase with the higher intensity to the next claim. In the case of n-order (n ≥ 3) phase-type distributed interclaim times, an iteration algorithm is presented to show that the optimal phase-wise barrier strategy is optimal among all dividend policies. We also find a similar conclusion like in the case of 2–order, the phase with the highest barrier is the phase with the highest intensity to the next claim.