Utility based pricing and hedging of jump diffusion processes with a view to applications

We discuss utility based pricing and hedging of jump diffusion processes with emphasis on the practical applicability of the framework. We point out two difficulties that seem to limit this applicability, namely drift dependence and essential risk aversion independence. We suggest to solve these by a re-interpretation of the framework. This leads to the notion of an implied drift. We also present a heuristic derivation of the marginal indifference price and the marginal optimal hedge that might be useful in numerical computations.Comment: 23 pages, v2: publishe

Overview of (pro-)Lie group structures on Hopf algebra character groups

Character groups of Hopf algebras appear in a variety of mathematical and physical contexts. To name just a few, they arise in non-commutative geometry, renormalisation of quantum field theory, and numerical analysis. In the present article we review recent results on the structure of character groups of Hopf algebras as infinite-dimensional (pro-)Lie groups. It turns out that under mild assumptions on the Hopf algebra or the target algebra the character groups possess strong structural properties. Moreover, these properties are of interest in applications of these groups outside of Lie theory. We emphasise this point in the context of two main examples: The Butcher group from numerical analysis and character groups which arise from the Connes--Kreimer theory of renormalisation of quantum field theories.Comment: 31 pages, precursor and companion to arXiv:1704.01099, Workshop on "New Developments in Discrete Mechanics, Geometric Integration and Lie-Butcher Series", May 25-28, 2015, ICMAT, Madrid, Spai

Weak Poisson structures on infinite dimensional manifolds and hamiltonian actions

We introduce a notion of a weak Poisson structure on a manifold $M$ modeled on a locally convex space. This is done by specifying a Poisson bracket on a subalgebra \cA \subeq C^\infty(M) which has to satisfy a non-degeneracy condition (the differentials of elements of \cA separate tangent vectors) and we postulate the existence of smooth Hamiltonian vector fields. Motivated by applications to Hamiltonian actions, we focus on affine Poisson spaces which include in particular the linear and affine Poisson structures on duals of locally convex Lie algebras. As an interesting byproduct of our approach, we can associate to an invariant symmetric bilinear form $\kappa$ on a Lie algebra \g and a $\kappa$-skew-symmetric derivation $D$ a weak affine Poisson structure on \g itself. This leads naturally to a concept of a Hamiltonian $G$-action on a weak Poisson manifold with a \g-valued momentum map and hence to a generalization of quasi-hamiltonian group actions

The Relationship between Physical Growth and Infant Behavioral Development in Rural Guatemala

The present study investigated the relationship between a number of anthropometric indices and behavioral development during the first 2 years of life in rural Guatemala. Length and weight were the indices most strongly correlated with behavioral development. If the effect of the infant\u27s length and weight was statistically controlled for, none of the other anthropometric variables explained a significant proportion of the variance in behavioral development. Con- trolling for length (or weight) assessed at the same age as the behavioral assessment, length (or weight) for younger ages was not significantly correlated with behavioral development. Changes in length or weight over time were correlated with changes in behavioral performance. We were unable to explain the association between physical growth and behavioral development by a number of variables including gestational age, nutrient intake, prevalence of disease, and familial characteristics

Unitary Representations of Unitary Groups

In this paper we review and streamline some results of Kirillov, Olshanski and Pickrell on unitary representations of the unitary group \U(\cH) of a real, complex or quaternionic separable Hilbert space and the subgroup \U_\infty(\cH), consisting of those unitary operators $g$ for which g - \1 is compact. The Kirillov--Olshanski theorem on the continuous unitary representations of the identity component \U_\infty(\cH)_0 asserts that they are direct sums of irreducible ones which can be realized in finite tensor products of a suitable complex Hilbert space. This is proved and generalized to inseparable spaces. These results are carried over to the full unitary group by Pickrell's Theorem, asserting that the separable unitary representations of \U(\cH), for a separable Hilbert space \cH, are uniquely determined by their restriction to \U_\infty(\cH)_0. For the $10$ classical infinite rank symmetric pairs $(G,K)$ of non-unitary type, such as (\GL(\cH),\U(\cH)), we also show that all separable unitary representations are trivial.Comment: 42 page

Diversity and activity of marine bacterioplankton during a diatom bloom in the North Sea assessed by total RNA and pyrotag sequencing

A recent investigation of bacterioplankton communities in the German Bight towards the end of a diatomdominated spring phytoplankton bloom revealed pronounced successions of distinct bacterial clades. A combination of metagenomics and metaproteomics indicated that these clades had distinct substrate spectra and consumed different algal substrates. In this study we re-analyzed samples from the initial study by total community RNA (metatranscriptomics) and 16S rRNA gene amplicon sequencing. This complementary approach provided new insights into the community composition and expressed genes as well as the assessment of metabolic activity levels of distinct clades. Flavobacteria (genera Ulvibacter, Formosa, and Polaribacter), Alphaproteobacteria (SARI 1 clade and Rhodobacteraceae) and Gammaproteobacteria (genus Reinekea and SAR92 dade) were the most abundant taxa. Mapping of the metatranscriptome data on assembled and taxonomically classified metagenome data of the same samples substantiated that Formosa and Polaribacter acted as major algal polymer degraders, whereas Rhodobacteraceae and Reinekea spp. exhibited less specialized substrate spectra. In addition, we found that members of the Rhodobacteraceae and SAR92 clade showed high metabolic activity levels, which suggests that these clades played a more important role during the bloom event as indicated by their in situ abundances. (c) 2014 The Authors. Published by Elsevier B.V

A Mole for Warm Magnetic and Optical Measurements of LHC Dipoles

A new rotating coil probe (a mole) has been developed for the simultaneous measurement of the magnetic field and magnetic axis of warm superconducting LHC dipoles and associated corrector windings. The mole houses a radial rotating coil and travels inside the magnet aperture by means of an externally driven two-way traction belt. The coil is rotated by an on-board piezo motor, being tested in view of future devices for cold measurements as the only type of motor compatible with strong magnetic fields. A virtual light spot is generated in the coil center by a LED source. The position of this light spot is measured from the outside by a system including a telescope, a CCD camera and a DSP. Jigs on reference granite tables are used to transfer the optical measurements to the magnet fiducials. We describe here the main characteristics and performance of the mol