带有随机收益和扰动项的相依风险模型中有限时破产概率的渐近行为  

Asymptotic Behavior of the Finite-time Ruin Probability in a Dependent Risk Model with Stochastic Return and Perturbation

作　　者：杨洋[1] 陈少颖 程东亚[2] YANG Yang;CHEN Shaoying;CHENG Dongya(School of Statistics and Data Sciences,Nanjing Audit University,Nanjing,Jiangsu,211815,P.R.China;School of Mathematical Sciences,Soochow University,Suzhou,Jiangsu,215006,P.R.China)

机构地区：[1]南京审计大学统计与数据科学学院,南京江苏211815 [2]苏州大学数学科学学院,苏州江苏215006

出　　处：《数学进展》2022年第6期1119-1131,共13页Advances in Mathematics（China）

基　　金：国家社会科学基金(No.22BTJ060);教育部人文社会科学研究规划基金(No.20YJA910006);江苏省自然科学基金(No.BK20201396);江苏省高校自然科学研究重大项目(No.19KJA180003);江苏省研究生科研与实践创新计划项目(No.KYCX21_1939)。

摘　　要：本文考虑了一个带有随机收益和扰动项的一般连续时风险模型,其中,投资组合的价格收入过程被描述为几何非负Lévy过程,扰动项是一个实值随机过程,表示保险公司的额外净损失.在理赔额序列满足[J.Korean Statist.Soc.,2012,41(2):213-224]中的相依结构且共同分布是次指数分布的条件下,本文建立了有限时破产概率的渐近估计公式.所得的结果表明,具有次指数理赔额的模型中,有限时破产概率的渐近行为对于该相依结构和轻尾扰动项不敏感.Consider a general continuous-time risk model with stochastic return and perturbation,in which the price process of the investment portfolio is described as a geometric nonnegative Levy process,and the diffusion perturbation is modelled by a real-valued stochastic process reflecting the additional net loss of an insurer.This paper establishes an asymptotic formula for the finite-time ruin probability under the condition that the subexponential claims follow the dependence structure proposed in[J.Korean Statist.Soc.,2012,41(2):213-224].Our obtained result shows that the asymptotic behavior of the finite-time ruin probability is insensitive to such a dependence structure and the light-tailed perturbation in the risk model with subexponential claims.

关 键 词：一般连续时风险模型 有限时破产概率 渐近行为 次指数分布 相依结构 

分 类 号：O211.4[理学—概率论与数理统计]