We consider the classical Cramér-Lundberg risk model with claim sizes that are mixtures of phase-type and subexponential variables. Exploiting a specific geometric compound representation, we propose control variate techniques to efficiently simulate the ruin probability in this situation. The resulting estimators perform well for both small and large initial capital. We quantify the variance reduction as well as the efficiency gain of our method over another fast standard technique based on the classical Pollaczek-Khinchine formula. We provide a numerical example to illustrate the performance, and show that for more time-consuming conditional Monte Carlo techniques, the new series representation also does not compare unfavorably to the one based on the Pollaczek-Khinchine formula.

我们考虑经典的Cramér-Lundberg风险模型，其索赔额是相类型和次指数变量的混合。利用特定的几何复合表示形式，我们提出了控制变量技术来有效地模拟这种情况下的破坏概率。所得的估算器对于大小的初始资本都表现良好。我们基于传统的Pollaczek-Khinchine公式，通过另一种快速标准技术，对方法的方差减小以及效率增益进行了量化。我们提供了一个数值示例来说明性能，并表明对于更耗时的条件蒙特卡洛技术，新的序列表示也不会不利地与基于Pollaczek-Khinchine公式的表示形式相提并论。