控制变换尾下END序列随机和的广义精致大偏差

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

重尾场合下随机变量随机和的精致大偏差是现代金融保险学中一项重要研究课题.假定理赔序列为一列END同分布随机变量序列,带控制变换尾,理赔到来过程为一般计数过程,且与理赔序列相互独立,在更弱的条件下,将文献[5]等中所做的一致变换尾上的广义精致大偏差推广到控制变换尾上,得到相应的偏离均值的大偏差结果.

The precise large deviations of random sums in heavy-tailed random variables is an important research topic in modern insur-ance and finance.Let the claims be a sequence of END real-valued identically distributed random variables with dominated variation, the claims is common counting process and independent from its sequence.Under the weaker condition,the extended precise large deviations of random sums which had been done in the document[5 ]was promoted to dominated variation,the largest deviation of con-sequential deflection mean is acquired.