The theory of stable probability distributions and their domains of attraction is derived in a direct way(avoiding the usual route via infinitely divisible distributions) using Fourier transforms. Regularly varyingfunctions play an important role in the exposition.

The theory of stable probability distributions and their domains of attraction is derived in a direct way (avoiding the usual route via infinitely divisible distributions) using Fourier transforms. Regularly varying functions play an important role in the exposition.

The stability of the financial system at higher loss levels is either characterized by asymptotic dependence or asymptotic independence. If asymptotically independent, the dependency, when present, eventually dies out completely at the more extreme quantiles, as in case of the multivariate...

We characterize second order regular variation of the tail sum of F together with a balance condition on the tails interms of the behaviour of the characteristic function near zero.

It has been known for a long time that for bootstrapping the probability distribution of the maximum of a sample consistently, the bootstrap sample size needs to be of smaller order than the original sample size. See Jun Shao and Dongsheng Tu (1995), Ex. 3.9,p. 123. We show that the same is true...

Asymptotic tail probabilities for bivariate linear combinations of subexponential random variables are given. These results are applied to explain the joint movements of the stocks of reinsurers. Portfolio investment and retrocession practices in the reinsurance industry, for reasons of...

We give a sufficient condition for i.i.d. random variables X1,X2 in order to have P{X1-X2>x} ~ P{|X1|>x} as x tends to infinity. A factorization property for subexponential distributions is used in the proof. In a subsequent paper the results will be applied to model fragility of financial markets.

For samples of random variables with a regularly varying tail estimating the tail index has received much attention recently. For the proof of asymptotic normality of the tail index estimator second order regular variation is needed. In this paper we first supplement earlier results on...

Asymptotic tail probabilities for bivariate linear combinations of subexponential random variables are given. These results are applied to explain the joint movements of the stocks of reinsurers. Portfolio investment and retrocession practices in the reinsurance industry, for reasons of...