中文摘要：

分红问题是金融保险研究的重要内容之一。针对带扰动的马氏对偶风险模型,考虑了其随机观察下的边界分红问题。根据收益到达发生、分红发生和环境状态改变3个因素,利用重期望公式得到了破产前累积分红折现期望在不同初始盈余下所满足的积分-微分方程;进一步求得了在马氏过程仅有两个状态情形下收益为指数分布时的累积分红折现期望。

英文摘要：

The dividends problem is one of the important issues of Finance and Insurance research.This paper considers a border strategy dividends at random observation time in a type of Markov-modulated dual risk model. We use double expectation formula to derive integral-differential equations of the expected discounted dividends until ruin time according to three factors of occurrence of income arrival process,occurrence of dividends and the change of environment state. Further more,we derive the solution of the expected discounted dividends in two state cases when the income distribution is exponential.