Uniform asymptotics for finite-time ruin probability in some dependent compound risk models with constant interest rate  

带有常数利息率的相依复合风险模型中有限时破产概率的一致渐近性(英文)

作　　者：杨洋[1,2] 刘伟[3] 林金官[4] 张玉林[1] 

机构地区：[1]东南大学经济管理学院,南京210096 [2]南京审计学院数学与统计学院,南京210029 [3]新疆大学数学与系统科学学院,乌鲁木齐830046 [4]东南大学数学系,南京210096

出　　处：《Journal of Southeast University(English Edition)》2014年第1期118-121,共4页东南大学学报（英文版）

基　　金：The National Natural Science Foundation of China(No.11001052,11171065,71171046);China Postdoctoral Science Foundation(No.2012M520964);the Natural Science Foundation of Jiangsu Province(No.BK20131339);the Qing Lan Project of Jiangsu Province

摘　　要：Consider two dependent renewal risk models with constant interest rate. By using some methods in the risk theory, uniform asymptotics for finite-time ruin probability is derived in a non-compound risk model, where claim sizes are upper tail asymptotically independent random variables with dominatedly varying tails, claim inter-arrival times follow the widely lower orthant dependent structure, and the total amount of premiums is a nonnegative stochastic process. Based on the obtained result, using the method of analysis for the tail probability of random sums, a similar result in a more complex and reasonable compound risk model is also obtained, where individual claim sizes are specialized to be extended negatively dependent and accident inter-arrival times are still widely lower orthant dependent, and both the claim sizes and the claim number have dominatedly varying tails.考虑了2个带有常数利息率的相依更新风险模型.首先研究了非复合风险模型,其中索赔额是上尾渐近独立且带有控制变换尾分布的非负随机变量,索赔时间间隔是宽下象限相依的,保费收入过程是一个非负的随机过程,利用风险理论中的方法,得到了有限时破产概率在某个有界区间上的一致渐近性.在此基础上,利用随机和尾渐近性的分析方法,进一步研究获得了更为复杂且合理的复合相依更新风险模型中有限时破产概率的一致渐近性公式,其中单个索赔额特殊化为广义负相依的,并且事故时间间隔仍然保持宽下象限相依的,索赔额和索赔次数均为控制变换尾的.

关 键 词：compound and non-compound risk models finite-time ruin probability dominatedly varying tail uniformasymptotics random sums dependence structure 

分 类 号：O211.4[理学—概率论与数理统计]