We propose a parametric model for a bivariate stable Lévy process based on a Lévy copula as a dependence model. We estimate the parameters of the full bivariate model by maximum likelihood estimation. As an observation scheme we assume that we observe all jumps larger than some [epsilon]0 and...

In this article, we review the concept of a Lévy copula to describe the dependence structure of a bivariate compound Poisson process. In this first statistical approach we consider a parametric model for the Lévy copula and estimate the parameters of the full dependent model based on a maximum...

For the solution Y of a multivariate random recurrence model Yn=AnYn-1+[zeta]n in we investigate the extremal behaviour of the process , , for with z*=1. This extends results for positive matrices An. Moreover, we obtain explicit representations of the compound Poisson limit of point processes...

Let [psi]i(u) be the probability of ruin for a risk process which has initial reserve u and evolves in a finite Markovian environment E with initial state i. Then the arrival intensity is [beta]j and the claim size distribution is Bj when the environment is in state j[set membership, variant]E....

With the df F of the rv X we associate the natural exponential family of df's F[lambda] wheredF[lambda](x)=e[lambda]x dF(x)/Ee[lambda]Xfor . Assume [lambda][infinity]=sup [Lambda][less-than-or-equals, slant][infinity] does not lie in [Lambda]. Let [lambda][short up arrow][lambda][infinity], then...

Let be a discrete time moving average process based on i.i.d. symmetric random variables {Zt} with a common distribution function from the domain of normal attraction of a p-stable law (0 p 2). We derive the limit distribution of the normalized periodogram . This generalizes the classical...

We consider Poisson shot noise processes that are appropriate to model stock prices and provide an economic reason for long-range dependence in asset returns. Under a regular variation condition we show that our model converges weakly to a fractional Brownian motion. Whereas fractional Brownian...