利率相依的离散索赔双险种风险模型  

Discrete claim double insurance risk model with interest rate dependence

作　　者：黎可 唐志飘 毕文毅 谢永钦 LI Ke;TANG Zhipiao;BI Wenyi;XIE Yongqin(School of General Education,Hunan University of Information Technology,Changsha,Hunan 410151,China;School of Mathematics and Statistics,Changsha University of Science&Technology,Changsha,Hunan 410114,China)

机构地区：[1]湖南信息学院通识教育学院,长沙410151 [2]长沙理工大学数学与统计学院,长沙410114

出　　处：《湖南城市学院学报（自然科学版）》2023年第4期61-66,共6页Journal of Hunan City University:Natural Science

基　　金：教育部高等教育司产学合作协同育人项目(202101170005);湖南省社会科学成果评审委员会课题(XSP2023JYC277,XSP21YBC368)。

摘　　要：波动利率是影响保险业经营的外生变量之一,它会通过影响承保利润、投资收益等不同途径影响保险公司的运作机制和运营效率,而险种多元化是目前保险公司经营的现状与发展趋势.本文从经典风险模型出发,探讨在利率变化、多险种情形下的保险公司破产概率及其相关问题.首先,采用随机分析理论与方法,建立了当利率满足一阶自回归结构时的利率相依的离散索赔双险种风险模型;其次,根据保费到达时间的不同,分别推导出该风险模型下的保险公司破产概率以及破产时盈余与赤字分布所满足的积分递推方程;最后,结合实际数值案例进行了分析.Fluctuating interest rate is one of the exogenous variables that affects the operation of insurance industry,which will affect the operation mechanism and efficiency of insurance companies through different paths such as premium profit and investment returns.And the diversification of insurance types is the current situation and development trend of insurance companies.Based on the classical risk model,this paper discusses the bankruptcy probability of insurance companies and its related problems in the case of interest rate change and multi-insurance.First of all,by using the theory and method of stochastic analysis,a discrete claim double insurance risk model with interest rate dependence is established when the interest rate satisfies the first-order auto-regressive structure.Secondly,according to the different arrival time of the premium,the integral recursive equations of the ruin probability and the surplus and deficit distribution of the insurance company under the risk model are derived respectively.Finally,the obtained results were demonstrated through specific practical examples.

关 键 词：波动利率 双险种 风险模型 破产概率 

分 类 号：O211.6[理学—概率论与数理统计]