【作者】 王楚；

【导师】 孔繁超；

【作者基本信息】 安徽大学 ， 概率论与数理统计， 2007， 硕士

【摘要】 本文在经典的风险模型的基础上，从实际需要出发，对其进行各种各样的改造，同时考虑了重尾和轻尾的两种情况，得出了关于破产概率和大偏差的几个结果。在第二章中，考虑了带干扰的双泊松风险模型，在C族中，得到了其上的大偏差的结论。进一步，考虑了一个较小的子族GERV族，也得出了其上的大偏差及一些相关的结论。在第三章中，首先，我们引入了广义齐次泊松过程的概念，在假定索赔和投保次数皆为广义齐次泊松过程的情况下，建立了带干扰的双广义复合泊松风险模型，运用鞅的方法，得出了它的破产概率和Lundberg不等式。此后，我们又考虑了索赔和投保次数为非齐次泊松过程的情形，得出了其破产概率一个比较弱的上界不等式。在第四章中，首先我们介绍了普通更新风险模型，并将其改造为复合更新风险模型，得出了其破产概率满足的一个等价式。更多还原

【Abstract】 This dissertation is based on the classical risk model. But we modify it with some kinds of methods according to reality’s demand. At the same time, we consider the difference of heavy-tailed and light-tailed and get some conclusions about ruin probabilitie and large deviations.In chapter 2, we build the double Poisson risk model and get the conclusion on its large deviation in class C. Moreover, we introduce a smaller heavy-tailed class (class GERV). Then we get the same conclusion of large deviation and some correlative conclusions, too.In chapter 3, at first, we introduce the concept of generalized homogeneous Poisson process. In the last, we get its final ruin probabilities and Lundberg inequality by martingale method. In addition, we consider the situation that the numbers of claims and policies are non-homogeneous Poisson process and get a weak upper bound inequality of its probability.In chapter 4, we introduce the ordinary renewal risk model firstly. Then we change it to compound renewal risk model. At last, we get a equivalence relation of its probability..更多还原