56 research outputs found

    Nonlinear Parabolic Equations arising in Mathematical Finance

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    This survey paper is focused on qualitative and numerical analyses of fully nonlinear partial differential equations of parabolic type arising in financial mathematics. The main purpose is to review various non-linear extensions of the classical Black-Scholes theory for pricing financial instruments, as well as models of stochastic dynamic portfolio optimization leading to the Hamilton-Jacobi-Bellman (HJB) equation. After suitable transformations, both problems can be represented by solutions to nonlinear parabolic equations. Qualitative analysis will be focused on issues concerning the existence and uniqueness of solutions. In the numerical part we discuss a stable finite-volume and finite difference schemes for solving fully nonlinear parabolic equations.Comment: arXiv admin note: substantial text overlap with arXiv:1603.0387

    Four years of Ulysses dust data: 1996 to 1999

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    The Ulysses spacecraft is orbiting the Sun on a highly inclined ellipse (i=79 i = 79^{\circ}, perihelion distance 1.3 AU, aphelion distance 5.4 AU). Between January 1996 and December 1999 the spacecraft was beyond 3 AU from the Sun and crossed the ecliptic plane at aphelion in May 1998. In this four-year period 218 dust impacts were recorded with the dust detector on board. We publish and analyse the complete data set of both raw and reduced data for particles with masses 1016g\rm 10^{-16} g to 108\rm 10^{-8} g. Together with 1477 dust impacts recorded between launch of Ulysses and the end of 1995 published earlier \cite{gruen1995c,krueger1999b}, a data set of 1695 dust impacts detected with the Ulysses sensor between October 1990 and December 1999 is now available. The impact rate measured between 1996 and 1999 was relatively constant with about 0.2 impacts per day. The impact direction of the majority of the impacts is compatible with particles of interstellar origin, the rest are most likely interplanetary particles. The observed impact rate is compared with a model for the flux of interstellar dust particles. The flux of particles several micrometers in size is compared with the measurements of the dust instruments on board Pioneer 10 and Pioneer 11 beyond 3 AU (Humes 1980, JGR, 85, 5841--5852, 1980). Between 3 and 5 AU, Pioneer results predict that Ulysses should have seen five times more (10μm\rm \sim 10 \mu m sized) particles than actually detected.Comment: accepted by Planetary and Space Science, 22 pages, 8 figures (1 colour figure

    Genetic insights into resting heart rate and its role in cardiovascular disease.

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    Resting heart rate is associated with cardiovascular diseases and mortality in observational and Mendelian randomization studies. The aims of this study are to extend the number of resting heart rate associated genetic variants and to obtain further insights in resting heart rate biology and its clinical consequences. A genome-wide meta-analysis of 100 studies in up to 835,465 individuals reveals 493 independent genetic variants in 352 loci, including 68 genetic variants outside previously identified resting heart rate associated loci. We prioritize 670 genes and in silico annotations point to their enrichment in cardiomyocytes and provide insights in their ECG signature. Two-sample Mendelian randomization analyses indicate that higher genetically predicted resting heart rate increases risk of dilated cardiomyopathy, but decreases risk of developing atrial fibrillation, ischemic stroke, and cardio-embolic stroke. We do not find evidence for a linear or non-linear genetic association between resting heart rate and all-cause mortality in contrast to our previous Mendelian randomization study. Systematic alteration of key differences between the current and previous Mendelian randomization study indicates that the most likely cause of the discrepancy between these studies arises from false positive findings in previous one-sample MR analyses caused by weak-instrument bias at lower P-value thresholds. The results extend our understanding of resting heart rate biology and give additional insights in its role in cardiovascular disease development

    The Galactic Environment of the Sun: Interstellar Material Inside and Outside of the Heliosphere

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