Abstract Asymptotic expansions for the tails of sums of random variables with regularly varying tails are mainly derived in the case of identically distributed random variables or in the case of random variables with the same tail index. Moreover, the higher-order terms are often given under...

The tail of the distribution of a sum of a random number of independent and identically distributed nonnegative random variables depends on the tails of the number of terms and of the terms themselves. This situation is of interest in the collective risk model, where the total claim size in a...

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...

We present two new classes of stationary max-stable random fields. For the first class, we use the spectral representation due to Schlather (2002) and assume that the stationary process used in the representation is proportional to a power of a max-stable random field. We derive the finite...

The tail of the distribution of a sum of a random number of independent and identically distributed nonnegative random variables depends on the tails of the number of terms and of the terms themselves. This situation is of interest in the collective risk model, where the total claim size in a...