具有随机投资收益过程的风险模型有限时间破产概率的一致渐近估计  

Uniform Asymptotic Estimate for the Finite-Time Ruin Prob-ability in a Risk Model with Stochastic Investment Returns

作　　者：程铭 王定成[1] CHENG Ming;WANG Dingcheng(School of Mathematical Sciences,University of Electronic Science and Technology of China,Chengdu,611731,China)

机构地区：[1]电子科技大学数学科学学院,成都611731

出　　处：《应用概率统计》2024年第4期558-571,共14页Chinese Journal of Applied Probability and Statistics

基　　金：国家自然科学基金项目(批准号:71271042)资助.

摘　　要：本文考虑一类利用càdlàg过程刻画保险盈余的随机投资收益,并利用二元上尾独立刻画保险索赔额之间相依结构的保险风险模型.一方面,本文提出条件(6),在此条件下得到该风险模型有限时间破产概率的一致渐近估计式.另一方面,考虑到条件(6)的普适性,本文发现很多重要的随机过程都满足条件(6),如Lévy过程,Vasicek模型,Cox-Ingersoll-Ross(CIR)模型和Heston模型.This paper establishes a risk model for an insurer with càdlàg investment returns and heavy-tailed claim sizes which are bivariate upper tail independent.On one hand,we propose condition(6),under which a uniform asymptotic estimate of the finite-time ruin probability in the risk model is obtained.On the other hand,considering the universality of condition(6),we find that the condition(6)can be easily verified by some important stochastic processes,such as the Lévy process,Vasicek model,Cox-Ingersoll-Ross(CIR)model,and Heston model.

关 键 词：渐近式 一致性 随机收益 破产概率 风险模型 

分 类 号：O211.4[理学—概率论与数理统计]