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 −∞...

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...

ch. 1. Decisions : the unit of success -- ch. 2. BYO -- ch. 3. Action to transaction to interaction -- ch. 4. The changing nature of data -- ch. 5. Social analytics -- ch. 6. Networked decisions -- ch. 7. Informed decisions -- ch. 8. Decisions as interactions -- ch. 9. Social listening -- ch....

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....

We analysed daily returns of the CRSP value weighted and equally weighted indices over 1953-2007 in order to test for Merton's theorised relationship between risk and return. Like some previous studies we used a GARCH stochastic volatility approach, employing not only traditional discrete time...

This paper proposes two related approximation schemes, based on a discrete grid on a finite time interval [0,T], and having a finite number of states, for a pure jump Lévy process Lt. The sequences of discrete processes converge to the original process, as the time interval becomes finer and...