中文摘要：

本文借助逐段决定马氏过程（PDMP）广义生成算子理论,寻求求解PDMP期望折扣罚函数φ（u）的新方法,得到了推导φ（u）满足的（脉冲）积分微分方程通用的一种程式化方法.特别地,对连续时间复合二项风险模型,得到了φ（u）满足的一个迭代公式,并对索赔额服从几何分布的特例得到了破产概率的准确表达式.

英文摘要：

This paper is intended to develop a new approach of deriving the （impulse） integro-differential equation, satisfied by the expected discounted penalty functionφ（u） for a piecewise deterministic Markov process （PDMP）, by virtue of the theory of the extended generator for PDMPs, In particular, a recursive equation is obtained for the expected discounted penalty function at ruin in the continuous-time compound binomial model. Furthermore, an exact solution of ruin probability is got in the case of a geometrical individual claim amount distribution.