Recent models of the insurance risk process use a Lévy process to generalise the traditional Cramér–Lundberg compound Poisson model. This paper is concerned with the behaviour of the distributions of the overshoot and undershoots of a high level, for a Lévy process which drifts to −∞...

We demonstrate the existence of models of the term structure of interest rates in which various forms of the expectations hypothesis hold. The new feature of these examples, which distinguishes them from those constructed by McCulloch, Riedel, and Fisher and Gilles, is that the spot rate is...

Let Xi be non-degenerate i.i.d. random variables with distribution function F, and let Xn1,...,Xnn denote the order statistics of X1,...,Xn. In trying to robustify the sample mean as an estimator of location, several alternatives have been suggested which have the intuitive appeal of being less...

In this paper, we discuss the application of quasi-Monte Carlo methods to the Heston model. We base our algorithms on the Broadie-Kaya algorithm, an exact simulation scheme for the Heston model. As the joint transition densities are not available in closed-form, the Linear Transformation method...

In this paper, we discuss the application of quasi-Monte Carlo methods to the Heston model. We base our algorithms on the Broadie-Kaya algorithm, an exact simulation scheme for the Heston model. As the joint transition densities are not available in closed-form, the Linear Transformation method...

We give a necessary and sufficient condition for a d-dimensional Lévy process to be in the matrix normalized domain of attraction of a d-dimensional normal random vector, as t↓0. This transfers to the Lévy case classical results of Feller, Khinchin, Lévy and Hahn and Klass for random walks....

The discrete-time GARCH methodology which has had such a profound influence on the modelling of heteroscedasticity in time series is intuitively well motivated in capturing many `stylized facts' concerning financial series, and is now almost routinely used in a wide range of situations, often...

The autoregressive--ARCH (AR--ARCH) and autoregressive--GARCH (AR--GARCH) models, which allow for conditional heteroskedasticity and autoregression, reduce to random walk or white noise for some values of the parameters. We consider generalized versions of the AR--ARCH(1) and AR--GARCH(1,1)...