Asymptotic Distributions of the Overshoot and Undershoots for the L\'evy Insurance Risk Process in the Cram\'er and Convolution Equivalent Cases

Recent models of the insurance risk process use a L\'evy process to generalise the traditional Cram\'er-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 L\'{e}vy process which drifts to $-\infty$ and satisfies a Cram\'er or a convolution equivalent condition. We derive these asymptotics under minimal conditions in the Cram\'er case, and compare them with known results for the convolution equivalent case, drawing attention to the striking and unexpected fact that they become identical when certain parameters tend to equality. Thus, at least regarding these quantities, the "medium-heavy" tailed convolution equivalent model segues into the "light-tailed" Cram\'er model in a natural way. This suggests a usefully expanded flexibility for modelling the insurance risk process. We illustrate this relationship by comparing the asymptotic distributions obtained for the overshoot and undershoots, assuming the L\'evy process belongs to the "GTSC" class

A Wiener--Hopf Monte Carlo simulation technique for L\'{e}vy processes

We develop a completely new and straightforward method for simulating the joint law of the position and running maximum at a fixed time of a general L\'{e}vy process with a view to application in insurance and financial mathematics. Although different, our method takes lessons from Carr's so-called "Canadization" technique as well as Doney's method of stochastic bounds for L\'{e}vy processes; see Carr [Rev. Fin. Studies 11 (1998) 597--626] and Doney [Ann. Probab. 32 (2004) 1545-1552]. We rely fundamentally on the Wiener-Hopf decomposition for L\'{e}vy processes as well as taking advantage of recent developments in factorization techniques of the latter theory due to Vigon [Simplifiez vos L\'{e}vy en titillant la factorization de Wiener-Hopf (2002) Laboratoire de Math\'{e}matiques de L'INSA de Rouen] and Kuznetsov [Ann. Appl. Probab. 20 (2010) 1801--1830]. We illustrate our Wiener--Hopf Monte Carlo method on a number of different processes, including a new family of L\'{e}vy processes called hypergeometric L\'{e}vy processes. Moreover, we illustrate the robustness of working with a Wiener--Hopf decomposition with two extensions. The first extension shows that if one can successfully simulate for a given L\'{e}vy processes then one can successfully simulate for any independent sum of the latter process and a compound Poisson process. The second extension illustrates how one may produce a straightforward approximation for simulating the two-sided exit problem.Comment: Published in at http://dx.doi.org/10.1214/10-AAP746 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Not the End of the Story:Floris Balthasars’ Map of the Siege of Grave (1602) as a Book Illustration for <i>Den Nassauschen Lauren-Crans </i>(1610)

Central to this article are two maps by Floris Balthasarsz van Berckenrode, both on the siege of Grave (1602) by Maurice of Orange during the Dutch Revolt. The first map was in 1602 produced as a news map about the events, the second was a re-edition, published eight years later as a book illustration for Jan Jansz Orlers, Den Nassauschen Lauren-Crans (Leiden 1610). In this article, principles for a new method are introduced to analyse and compare these ‘story maps’ with particular attention to the narrative impact of the map. Using this method in combi-nation with (book) historical research, it argues that the 1610 map should be considered as a ‘memorial map’ that reframes the collective memory of the Dutch Revolt. It emphasizes the dynamic relationship between news, map and book publishing and pleads for a more prominent position of story maps and book illustrations in Early Modern memory landscapes

A Low Noise Amplifier Optimized for a GPS Receiver RF Front End

A cascode LNA was optimized for a GPS receiver radio frequency front end using a 0.18 μm CMOS technology. By careful choice of device geometry, gate and source degeneration inductors, a fully integrated LNA can be optimized to have a low noise figure, a high voltage gain and a wide dynamic range. The optimized LNA has a 1.512 dB noise figure, a –42.05 dB S11, a 20.04 dB voltage gain a –19.82 dB input referred 1-db compression point and a –5.49 dBm third order input intercept point, with a 11.6 mW power consumption

Energy Savings from Implementing Collaborative Beamforming for a Remote Low Power Wireless Sensor Network

This paper outlines the implementation of collaborative beamforming to a remote low power wireless sensor network and presents its energy saving potential. The directivity procured from the beamforming allows power to be saved, which is distributed over the network. This allows each sensor within the network to have the same prolonged lifetime, and thus create a long lasting reliable network. The associated overhead with collaborative beamforming is in conjunction examined, where Single Frequency Networks (SFN) are taken as reference for synchronisation procedures. Finally, the influences of various network operating parameters on the energy benefit that can be obtained from collaborative beamforming in respect to network sizes are presented

Acute dystonic reaction to metoclopramide in patients carrying homozygous cytochrome P450 2D6 genetic polymorphisms

BACKGROUND: Extrapyramidal syndromes (EPS) are clinically relevant side effects of metoclopramide which are often not anticipated. PATIENTS AND METHODS: Two patients who received metoclopramide developed an acute dystonic reaction. Symptoms disappeared after biperiden or trihexyphenidyl were given. Molecular analysis of the CYP2D6 gene was performed using a PCR-based method. RESULTS: Both patients were homozygous for inactive CYP2D6 alleles (CYP2D6*4/*4 and CYP2D6*4/*5), which are associated with slow drug metabolism. CONCLUSION: Metoclopramide-induced acute dystonic reactions may occur in patients carrying a CYP2D6 genetic polymorphism