带投资的多险种复合风险模型及其破产概率的研究  

Ruin Probability under the Compound Multi-risk Model with Investment

作　　者：徐嗣棪 徐汇知 XU Siyan;XU Huizhi(Col.of Science,North China Univ.of Tech.,100144,Beijing,China)

机构地区：[1]北方工业大学理学院

出　　处：《北方工业大学学报》2019年第5期37-42,50,共7页Journal of North China University of Technology

基　　金：北京市市属高校基本科研业务费项目“大数据的统计学基础理论与分析方法”(110052971921/103)

摘　　要：经典风险模型往往只考虑了保险公司存在整体收益和集体索赔,与实际情况不符.本文在文献研究基础上,考虑带投资的多险种模型下保险公司的破产概率问题.将保费到达和索赔过程均为复合Poisson-Geometric过程的风险模型推广为带干扰、带投资的多险种风险模型,运用鞅理论得出满足Lundberg不等式的破产概率的表达式.In the classical risk model,only the whole income and collective claim of the insurance company are considered,which is inconsistent with the actual situation.On the basis of literature research,this paper considers the bankruptcy probability of insurance companies under the multi-risk model with investment.The conditions of risk model in which premium arrival process and claim process are composite Poisson-Geometric process are broadened.This paper promotes the model as a multi-risk model with interference and investment,using martingale theory to get the expression of ruin probability,and it satisfies the Lundberg inequality.

关 键 词：扰动风险模型 复合POISSON-GEOMETRIC过程 破产概率 

分 类 号：O211.6[理学—概率论与数理统计]