相依赔付带投资的延迟风险模型的极限性质  

Limit property of the delayed risk model under dependent claims and investment

作　　者：肖鸿民 刘爱玲 何艳 Xiao Hong-min Liu Ai-ling He Yan(School of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Chin)

机构地区：[1]西北师范大学数学与统计学院,兰州730070

出　　处：《兰州大学学报（自然科学版）》2017年第5期696-700,705,共6页Journal of Lanzhou University(Natural Sciences)

基　　金：国家自然科学基金项目(71261023)

摘　　要：研究了带投资的延迟索赔风险模型破产概率的极限性质.保险公司将其资产按常数比例投资于满足几何布朗运动的股票市场,其余部分投资于非负利率的债券市场.在主索赔额和延迟索赔额序列分别为负相依且属于重尾分布族的情形下,得到了有限时间破产概率的渐近等价表达式.该结论的有效性由相应的数值模拟进行了很好地验证,为保险公司的投资提供了一种思路.The limit property of ruin probability on the delayed risk model with investment was investigated. The case of an insurance company allowed to invest a constant fraction of its wealth in a stock market which was described by a geometric Brownian motion,while the remaining wealth in a bond with a nonnegative interest force. Under the assumptions that the sequences of the main and delayed claims were negatively dependent random variables and belonged to the heavy-tailed distribution class respectively, asymptotic formulas of finite-time ruin probability were obtained. The effectiveness of the results was remarkably verified by a numerical simulation. The conclusion of this paper can provide a kind of investment idea for insurance company.

关 键 词：延迟风险模型 负相依 重尾分布族 几何布朗运动 有限时间破产概率 

分 类 号：O211.4[理学—概率论与数理统计]