本文考虑随机利率下相依索赔的离散风险模型,模型中假设每次主索赔可能引起一次副索赔,而每次副索赔有可能延迟发生,当资产盈余达到边界b时,公司给投保者分发一定红利;考虑预期红利的现值时,假设利率服从一有限状态空间的马尔可夫链,我们得到了破产前预期累积分红所满足的差分方程及特殊索赔情形下预期累积分红现值的精确解析式,并结合实例进行了数值模拟. In this paper, we consider the discrete risk model of dependent claim under random interest rate. In the model, it is assumed that each main claim may cause a secondary claim, and each time a secondary claim may be delayed. When the asset surplus reaches the boundary b, the company distributes certain bonus to the insured When we consider the present value of the expected dividend, assuming that the interest rate obeys a Markov chain of a finite state space, we obtain the exact analytic formula of the difference equation and the present value of expected cumulative dividend under the special claim scenario, The numerical simulation is carried out with examples.