On extremal behavior of aggregation of largest claims

In 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) Asimit, A.V., Hashorva, E., Kortschak, D. (2012). Exact tail asymptotics of the total loss of largest claim reinsurance treaties. Available at SSRN: http://ssrn.com/abstract=1993114 or http://dx.doi.org/10.2139/ssrn.1993114. Google Scholar].