中文摘要：

考虑审核时间间隔为混合指数分布时的期望贴现罚金函数，利用全概率公式和Laplace变换。给出贴现罚金函数满足的积分微分方程以及更新方程．针对指数索赔的情况给出期望贴现罚金函数的计算过程．最后，给出一些破产相关数据，以解释随机观察的效果．

英文摘要：

The discounted penalty function of compound Poisson risk model is studied when observation interval is mixed exponential distribution. By using tatal probability formula and Laplace transform, the integral differential equation for discounted penalty function and renewal equation are given. The calculation process of the discounted penalty function is given for the case of exponention claims. Some data about ruin are given to illustrate the effect of random observation times.