Local risk-minimization under the benchmark approach

© 2014, Springer-Verlag Berlin Heidelberg. We study the pricing and hedging of derivatives in incomplete financial markets by considering the local risk-minimization method in the context of the benchmark approach, which will be called benchmarked local risk-minimization. We show that the proposed benchmarked local risk-minimization allows to handle under extremely weak assumptions a much richer modeling world than the classical methodology

Unfolding the Hierarchy of Voids

We present a framework for the hierarchical identification and characterization of voids based on the Watershed Void Finder. The Hierarchical Void Finder is based on a generalization of the scale space of a density field invoked in order to trace the hierarchical nature and structure of cosmological voids. At each level of the hierarchy, the watershed transform is used to identify the voids at that particular scale. By identifying the overlapping regions between watershed basins in adjacent levels, the hierarchical void tree is constructed. Applications on a hierarchical Voronoi model and on a set of cosmological simulations illustrate its potential.Comment: 5 pages, 2 figure

The Cosmically Depressed: Life, Sociology and Identity of Voids

We review and discuss aspects of Cosmic Voids that form the background for our Void Galaxy Survey (see accompanying paper by Stanonik et al.). Following a sketch of the general characteristics of void formation and evolution, we describe the influence of the environment on their development and structure and the characteristic hierarchical buildup of the cosmic void population. In order to be able to study the resulting tenuous void substructure and the galaxies populating the interior of voids, we subsequently set out to describe our parameter free tessellation-based watershed void finding technique. It allows us to trace the outline, shape and size of voids in galaxy redshift surveys. The application of this technique enables us to find galaxies in the deepest troughs of the cosmic galaxy distribution, and has formed the basis of our void galaxy program.Comment: 10 pages, 4 figures, proceedings "Galaxies in Isolation" (May 2009, Granada, Spain), eds. L. Verdes-Montenegro, ASP (this is a colour, extended and combined version; accompanying paper to Stanonik et al., arXiv:0909.2869, in same volume

Alignments of Voids in the Cosmic Web

We investigate the shapes and mutual alignment of voids in the large scale matter distribution of a LCDM cosmology simulation. The voids are identified using the novel WVF void finder technique. The identified voids are quite nonspherical and slightly prolate, with axis ratios in the order of c:b:a approx. 0.5:0.7:1. Their orientations are strongly correlated with significant alignments spanning scales >30 Mpc/h. We also find an intimate link between the cosmic tidal field and the void orientations. Over a very wide range of scales we find a coherent and strong alignment of the voids with the tidal field computed from the smoothed density distribution. This orientation-tide alignment remains significant on scales exceeding twice the typical void size, which shows that the long range external field is responsible for the alignment of the voids. This confirms the view that the large scale tidal force field is the main agent for the large scale spatial organization of the Cosmic Web.Comment: 10 pages, 4 figures, submitted to MNRAS, for high resolution version, see http://www.astro.rug.nl/~weygaert/tim1publication/voidshape.pd

The Spine of the Cosmic Web

We present the SpineWeb framework for the topological analysis of the Cosmic Web and the identification of its walls, filaments and cluster nodes. Based on the watershed segmentation of the cosmic density field, the SpineWeb method invokes the local adjacency properties of the boundaries between the watershed basins to trace the critical points in the density field and the separatrices defined by them. The separatrices are classified into walls and the spine, the network of filaments and nodes in the matter distribution. Testing the method with a heuristic Voronoi model yields outstanding results. Following the discussion of the test results, we apply the SpineWeb method to a set of cosmological N-body simulations. The latter illustrates the potential for studying the structure and dynamics of the Cosmic Web.Comment: Accepted for publication HIGH-RES version: http://skysrv.pha.jhu.edu/~miguel/SpineWeb

A Dynamical Classification of the Cosmic Web

A dynamical classification of the cosmic web is proposed. The large scale environment is classified into four web types: voids, sheets, filaments and knots. The classification is based on the evaluation of the deformation tensor, i.e. the Hessian of the gravitational potential, on a grid. The classification is based on counting the number of eigenvalues above a certain threshold, lambda_th at each grid point, where the case of zero, one, two or three such eigenvalues corresponds to void, sheet, filament or a knot grid point. The collection of neighboring grid points, friends-of-friends, of the same web attribute constitutes voids, sheets, filaments and knots as web objects. A simple dynamical consideration suggests that lambda_th should be approximately unity, upon an appropriate scaling of the deformation tensor. The algorithm has been applied and tested against a suite of (dark matter only) cosmological N-body simulations. In particular, the dependence of the volume and mass filling fractions on lambda_th and on the resolution has been calculated for the four web types. Also, the percolation properties of voids and filaments have been studied. Our main findings are: (a) Already at lambda_th = 0.1 the resulting web classification reproduces the visual impression of the cosmic web. (b) Between 0.2 < lambda_th < 0.4, a system of percolated voids coexists with a net of interconected filaments. This suggests a reasonable choice for lambda_th as the parameter that defines the cosmic web. (c) The dynamical nature of the suggested classification provides a robust framework for incorporating environmental information into galaxy formation models, and in particular the semi-analytical ones.Comment: 11 pages, 6 figures, submitted to MNRA

Crawling the Cosmic Network: Identifying and Quantifying Filamentary Structure

We present the Smoothed Hessian Major Axis Filament Finder (SHMAFF), an algorithm that uses the eigenvectors of the Hessian matrix of the smoothed galaxy distribution to identify individual filamentary structures. Filaments are traced along the Hessian eigenvector corresponding to the largest eigenvalue, and are stopped when the axis orientation changes more rapidly than a preset threshold. In both N-body simulations and the Sloan Digital Sky Survey (SDSS) main galaxy redshift survey data, the resulting filament length distributions are approximately exponential. In the SDSS galaxy distribution, using smoothing lengths of 10 h^{-1} Mpc and 15 h^{-1} Mpc, we find filament lengths per unit volume of 1.9x10^{-3} h^2 Mpc^{-2} and 7.6x10^{-4} h^2 Mpc^{-2}, respectively. The filament width distributions, which are much more sensitive to non-linear growth, are also consistent between the real and mock galaxy distributions using a standard cosmology. In SDSS, we find mean filament widths of 5.5 h^{-1} Mpc and 8.4 h^{-1} Mpc on 10 h^{-1} Mpc and 15 h^{-1} Mpc smoothing scales, with standard deviations of 1.1 h^{-1} Mpc and 1.4 h^{-1} Mpc, respectively. Finally, the spatial distribution of filamentary structure in simulations is very similar between z=3 and z=0 on smoothing scales as large as 15 h^{-1} Mpc, suggesting that the outline of filamentary structure is already in place at high redshift.Comment: 10 pages, 11 figures, accepted to MNRA