重尾索赔下变保费率干扰风险模型的大偏差

摘要

A perturbed risk model with variable premium rates and heavy-tailed claims was considered. The precise large deviation for the claim surplus process of this risk model was obtained by means of some relative theories in analysis and probability theory, when the claim process is a nonnegative inter-valued one and the distributions of heavy-tailed claims belong to the consistently varying category. Also, a result in Ref. [Wei X, Yu J, Hu Y. Large deviations and finite time ruin probability for perturbed risk with variable premium rate. Acta Mathematical Scientia, 2007,27(4): 616-623] was extended.%考虑一类重尾索赔下变保费率带干扰项的风险模型,当索赔到达过程为一般非负整值过程,索赔额的分布属于重尾分布一致变化族时,利用分析和概率的有关理论得到了索赔剩余过程的精细大偏差,从而推广了文献[Wei X,YuJ,Hu Y.Large deviations and finite time ruin probability for perturbed risk with variable premium rate.Acta Mathematical Scientia,2007,27(4):616-623]中有关结论.