具有投资收益的多险种复合负二项风险模型的破产概率  

Ruin probability of multi-type compound negative binomial risk model with investment profit

作　　者：魏静[1] 葛世刚[1] 仓定帮[1] 

机构地区：[1]华北科技学院基础部,北京东燕郊101601

出　　处：《华北科技学院学报》2017年第1期106-109,共4页Journal of North China Institute of Science and Technology

基　　金：廊坊市科技局科学技术研究与发展计划自筹经费项目(2016011031;2016011048;2016013113)

摘　　要：在经典风险模型的基础上,考虑到投保集体的不同质性,建立了保费收取过程和理赔过程均为负二项过程、投资收益率为常数的多险种随机风险模型,通过分析盈利过程的性质,得到终极破产概率的计算公式和破产概率上界的Lundberg不等式,特别地,给出了两险种时,保费和理赔额服从指数分布下破产概率的精确表达式。结果表明:在投资收益一定时,保险公司增加用于投资的金额,可以降低破产概率,从而规避风险。Based on classic risk model,considering the non homogeneity of the policyholders, a multiple sto- chastic risk model was established with negative binomial process for the premium collecting frequency and claim frequency and the rate of return on investment be constant. Through analyzing the properties of the profit process, it obtains the ultimate ruin probability and the Lundberg inequality formula of upper bound for ruin probability. In particularly, the exact expression of probability was obtained for two - type insurance with pre- miums and claims in exponential distribution. The results show that when the investment income is certain, the insurance company can reduce the ruin probability by increasing investment to avoid risks.

关 键 词：多险种 投资 负二项过程 指数分布 破产概率 

分 类 号：O211.6[理学—概率论与数理统计]