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