Significance and limitations of the VAR figures publicly disclosed by large financial institutions.

The value-at-risk (VAR) figures publicly disclosed by the major banks provide useful information on the market risk taken by the banking system. But a number of methodological precautions need to be taken when analysing these figures. These are detailed in this article. The assumptions underlying VAR calculations can, indeed, differ from one institution to the next and are rarely very explicit. The conclusions to be drawn from these figures should therefore be treated with caution. The information provided by disclosed VARs should be corroborated by other indicators and analysed against the general macro-fi nancial backdrop. When they point to greater risk exposures, these figures act as warning signals for conducting more in-depth analyses of the vulnerabilities that could affect financial stability. VAR figures disclosed by financial institutions are closely monitored by central banks and are, for example, often discussed in the overview of the Banque de France’s Financial Stability Review. These figures have contributed to supporting our assessment of a rise in market risk exposures at the time when short-term interest rates were uniformly very low, before the Fed started raising its key rates, which called for heightened vigilance even though the macro-financial context appeared favourable. Central banks’ constant concerns about greater transparency on the part of financial institutions resulted in the publication of the Fisher II report. In this framework, one way of strengthening financial stability would be to encourage credit institutions to be more transparent as regards their methods for calculating disclosed VARs. Credit institutions could, for instance, include more precise and easily comparable methodological explanations in their annual reports. This should not prevent the leading banks from setting up more sophisticated risk management techniques nor impinge on their communication policy. By authorising banks to use – subject to validation – an internal ratings-based approach for calculating their regulatory capital requirements, banking supervisors have actually acknowledged at the international level the diversity of markets and operations carried out by banks. This diversity implies adopting calculation methods tailored to the specificity and management techniques of each bank. Banks should in fact provide analysts with the most relevant information possible. But, in view of current practices, the level of transparency as regards the methods used is still insufficient. In addition, financial institutions other than banks, for example hedge funds, should also be encouraged to disclose their VAR figures. Lastly, financial institutions should disclose their stress tests on a more regular basis, as a methodological complement to the VAR figures, but also in order to prevent a potential homogenisation of behaviours which could result from an exclusive use of VARs in banks’ communication strategies.

Hopf instantons, Chern-Simons vortices, and Heisenberg ferromagnets

The dimensional reduction of the three-dimensional fermion-Chern-Simons model (related to Hopf maps) of Adam et el. is shown to be equivalent to (i) either the static, fixed--chirality sector of our non-relativistic spinor-Chern-Simons model in 2+1 dimensions, (ii) or a particular Heisenberg ferromagnet in the plane.Comment: 4 pages, Plain Tex, no figure

A theory of non-local linear drift wave transport

Transport events in turbulent tokamak plasmas often exhibit non-local or non-diffusive action at a distance features that so far have eluded a conclusive theoretical description. In this paper a theory of non-local transport is investigated through a Fokker-Planck equation with fractional velocity derivatives. A dispersion relation for density gradient driven linear drift modes is derived including the effects of the fractional velocity derivative in the Fokker-Planck equation. It is found that a small deviation (a few percent) from the Maxwellian distribution function alters the dispersion relation such that the growth rates are substantially increased and thereby may cause enhanced levels of transport.Comment: 22 pages, 2 figures. Manuscript submitted to Physics of Plasma

Toward mixed-element meshing based on restricted Voronoi diagrams

In this paper we propose a method to generate mixed-element meshes (tetrahedra, triangular prisms, square pyramids) for B-Rep models. The vertices, edges, facets, and cells of the final volumetric mesh are determined from the combinatorial analysis of the intersections between the model components and the Voronoi diagram of sites distributed to sample the model. Inside the volumetric regions, Delaunay tetrahedra dual of the Voronoi diagram are built. Where the intersections of the Voronoi cells with the model surfaces have a unique connected component, tetrahedra are modified to fit the input triangulated surfaces. Where these intersections are more complicated, a correspondence between the elements of the Voronoi diagram and the elements of the mixedelement mesh is used to build the final volumetric mesh. The method which was motivated by meshing challenges encountered in geological modeling is demonstrated on several 3D synthetic models of subsurface rock volumes

(In)finite extensions of algebras from their Inonu-Wigner contractions

The way to obtain massive non-relativistic states from the Poincare algebra is twofold. First, following Inonu and Wigner the Poincare algebra has to be contracted to the Galilean one. Second, the Galilean algebra is to be extended to include the central mass operator. We show that the central extension might be properly encoded in the non-relativistic contraction. In fact, any Inonu-Wigner contraction of one algebra to another, corresponds to an infinite tower of abelian extensions of the latter. The proposed method is straightforward and holds for both central and non-central extensions. Apart from the Bargmann (non-zero mass) extension of the Galilean algebra, our list of examples includes the Weyl algebra obtained from an extension of the contracted SO(3) algebra, the Carrollian (ultra-relativistic) contraction of the Poincare algebra, the exotic Newton-Hooke algebra and some others. The paper is dedicated to the memory of Laurent Houart (1967-2011).Comment: 7 pages, revtex style; v2: Minor corrections, references added; v3: Typos correcte

A Fractional Fokker-Planck Model for Anomalous Diffusion

In this paper we present a study of anomalous diffusion using a Fokker-Planck description with fractional velocity derivatives. The distribution functions are found using numerical means for varying degree of fractionality observing the transition from a Gaussian distribution to a L\'evy distribution. The statistical properties of the distribution functions are assessed by a generalized expectation measure and entropy in terms of Tsallis statistical mechanics. We find that the ratio of the generalized entropy and expectation is increasing with decreasing fractionality towards the well known so-called sub-diffusive domain, indicating a self-organising behavior.Comment: 22 pages, 14 figure

The fractional Schr\"{o}dinger operator and Toeplitz matrices

Confining a quantum particle in a compact subinterval of the real line with Dirichlet boundary conditions, we identify the connection of the one-dimensional fractional Schr\"odinger operator with the truncated Toeplitz matrices. We determine the asymptotic behaviour of the product of eigenvalues for the $\alpha$-stable symmetric laws by employing the Szeg\"o's strong limit theorem. The results of the present work can be applied to a recently proposed model for a particle hopping on a bounded interval in one dimension whose hopping probability is given a discrete representation of the fractional Laplacian.Comment: 10 pages, 2 figure