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Assume that claims in a portfolio of insurance contracts are described byindependent and identically distributed random variables with regularly varyingtails and occur according to a near mixed Poisson process. We provide acollection of results pertaining to the joint asymptotic Laplace transforms ofthe normalized sums of the smallest and largest claims, when the length of theconsidered time interval tends to infinity. The results crucially depend on thevalue of the tail index of the claim distribution, as well as on the number oflargest claims under consideration.

Joint asymptotic distributions of smallest and largest insurance claims