On extremal behavior of aggregation of largest claims

Abstract

ABSTRACTIn this paper some dependent risks are considered, and tail asymptotic probabilities for linear combinations of finite number or random number of randomly weighted order statistics are estimated under various assumptions, where the primary random variables have long and dominatedly varying tails. Our findings are highly motivated by the need of the investigation of extremal behavior of aggregation of large claims, which has been shown in Asimit et al. (2012).