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...

Consider a random walk or Lévy process {St} and let [tau](u) = inf {t[greater-or-equal, slanted]0 : St u}, P(u)(·) = P(· [tau](u) < [infinity]). Assuming that the upwards jumps are heavy-tailed, say subexponential (e.g. Pareto, Weibull or lognormal), the asymptotic form of the P(u)-distribution of the process {St} up to time [tau](u) is described as u --> [infinity]. Essentially, the results confirm the folklore that level crossing occurs as result of one big jump. Particular sharp conclusions are obtained for...</[infinity]).>

We study the tail asymptotics of the r.v. X(T) where {X(t)} is a stochastic process with a linear drift and satisfying some regularity conditions like a central limit theorem and a large deviations principle, and T is an independent r.v. with a subexponential distribution. We find that the tail...

Motivated by empirical evidence of long range dependence in macroeconomic variables like interest rates we propose a fractional Brownian motion driven model to describe the dynamics of the short and the default rate in a bond market. Aiming at results analogous to those for affine models we...