D族END随机变量随机和的精致大偏差

Precise Large Deviations of Random Sums in the Presence of END Structure and Dominated Variation

重尾理赔下风险模型的精致大偏差研究是现代保险精算学中的一个重要课题。假定理赔序列为一列D族重尾END同分布随机变量序列,理赔到来过程为一与理赔序列独立的计数过程。在一定条件下,得到该风险模型在一般情形下的精致大偏差,推广了相关文献已报道的结果。

The risk model of precise large deviations for sums of heavy-tailed random variables is an important topic in insurance and finance. In this paper,let the claims be a sequence of real-valued identically distributed random variables with common distribution function. The claim number is a nonnegative inter-valued counting process independent of the claims. Under some conditions,we obtained precise large deviations of the risk model under the general case and promoted a number of classical results.