重尾索赔下带干扰风险模型破产概率的局部解  

The Asymptotic Relationships of the Ruin Probabilities in the Classic Risk Model Perturbed by Diffusion Under Heavy-tailed Claims

作　　者：龚日朝[1,2] 邹捷中[1] 

机构地区：[1]中南大学数学科学与计算技术学院 [2]湖南省产业经济研究基地,湘潭411201

出　　处：《应用数学学报》2007年第3期563-572,共10页Acta Mathematicae Applicatae Sinica

基　　金：湖南省自然科学基金(06JJ2019);湖南省社科基金(06YB63);湖南省教育厅优秀青年基金(06B34)资助项目.

摘　　要：著名的Embrechts-Goldie-Veraverbeke公式给出了在重尾索赔下Gramér-Lundberg风险模型关于破产概率的等价式,唐启鹤又给出了一个局部化的结果,本文将上述风险模型推广到带干扰的Gramér- Lundberg风险模型,得到了索赔分布F∈S^＊时破产概率局部解的等价式．虽然[9]也得到了同样的结果,但是[9]中犯了概念性的错误,本文指出了该错误,然后给予了严格的证明．In classic risk model the ruin probability satisfy R（x, ∞） - ρ^-1F^-e（x） if the claim sizes are heavy-tailed, where F^-e denotes the equilibrium distribution of the common d.f. F of the i.i.d, claims, p is the safity loading coefiencent of the model. Furtherly Tang Qihe obtained a related local asympotic relationship for the ruin probability, i.e. R（x, x＋z] ,- Z/ρμF^-（x） under the claim distribution F ∈ S^＊. In this paper,we consider the local asymptotic relationship of the ruin probability in the classic risk model perturbed by diffusion and obtain the same results as above under the F ∈ S^＊, too. Although this result has been obtained in [9], there was a critical wrong, so the wrong is pointed in our paper.

关 键 词：重尾分布 破产概率 扩散 风险模型 

分 类 号：O211.3[理学—概率论与数理统计] O213.2[理学—数学]