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)

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

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.

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.