中文摘要：

本文研究了在一类马氏相关更新风险模型中的红利-惩罚等式的问题.推导了在常数红利边界下,折扣惩罚函数满足的方程,利用解微分-积分方程的方法,更简洁的推出了红利-惩罚等式相关的结果,推广了文献[1]的结论.

英文摘要：

In this paper, a Markov renewal risk model with a constant dividend barrier is considered, the matrix form of systems of integro-differential equations is presented and theanalytical solutions to these systems are derived. By the general solution of the integro-differential equation, the dividend-penalty identity is obtained, which generalizes the results of the tel.[l].