具有两类索赔的风险过程的破产概率

古典风险模型主要考虑同一类型的风险构成的风险过程，研究当承保人承保两类不同的风险时，相应的风险总和构成的风险过程．在两类索赔计数过程均为Erlang（2）过程时，通过补充新的风险过程和相应的破产概率，通过考虑在首个指数时刻发生的不同情况，推导出破产概率所满足的微积分方程组，并就索赔额服从指数分布的情形得到了破产概率的精确表达式．最后利用更新方程还给出了不同类型破产概率的一个上界．这些结论的得出对于保险人评估风险具有重要的指导意义．

Ruin probabilities of risk model with two different risk classes

Classical risk model considers one class of risk mainly. The paper studied risk models consists of two different classes of risk and whose related aggregate claims process is the sum of two classes of claims. When the claim number processes are Erlang(2) ones, by adding new risk processes that are closely related to the original one and their relevant ruin probabilities, the first exponential epoch four integer-differential equations were obtained. The explicit expressions of the ruin probabilities were given when the claim sizes are exponentially distributed. The renewal theorem was used to get the upper bound of the ruin probability. These results are useful for insurers to analyze risks taken.