Let fX;Xi; i = 1; 2; :::g denote independent positive random variables having a common distribution function F(x) and, independent of X, let N denote an integer valued random variable. Using S(0) = 0 and S(n) = S(n ?? 1) + Xn, the random sum S(N) has distribution function G(x) = 1Xi=0 P(N =...

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...

Bocker and Kluppelberg [Risk Mag., 2005, December, 90-93] presented a simple approximation of OpVaR of a single operational risk cell. The present paper derives approximations of similar quality and simplicity for the multivariate problem. Our approach is based on the modelling of the dependence...

Let X and Y be two nonnegative dependent random variables according to a copula function. Under appropriate conditions, the closure property of the product XY is derived when X belongs to class S and R, respectively. Some examples are provided to illustrate the impact of the dependence structure...

Karamata’s theorem is well known, which examines the integral properties of regular variation functions. In this paper, we obtain the second-order version of Karamata’s theorem, and give its one application in characterizing the second-order regular variation property of a survival function...

Relay nodes in an ad hoc network can be modelled as fluid queues, in which the available service capacity is shared by the input and output. In this paper such a relay node is considered; jobs arrive according to a Poisson process and bring along a random amount of work. The total transmission...

Consider a tandem queue consisting of two single-server queues in series, with a Poisson arrival process at the first queue and arbitrarily distributed service times, which for any customer are identical in both queues. For this tandem queue, we relate the tail behaviour of the sojourn time...

Suppose are independent subexponential random variables with partial sums. We show that if the pairwise sums of the ’s are subexponential, then is subexponential and . The result is applied to give conditions under which as , where are constants such that is a.s. convergent. Asymptotic tail...

This paper establishes a simple asymptotic formula for the finite time ruin probability of a compound renewal risk model with constant interest force. We assume that the claim sizes are Weakly Negatively Dependent (WND) and identically distributed random variables belonging to the class of...