3,228 research outputs found
Suitability of Capital Allocations for Performance Measurement
Capital allocation principles are used in various contexts in which a risk
capital or a cost of an aggregate position has to be allocated among its
constituent parts. We study capital allocation principles in a performance
measurement framework. We introduce the notation of suitability of allocations
for performance measurement and show under different assumptions on the
involved reward and risk measures that there exist suitable allocation methods.
The existence of certain suitable allocation principles generally is given
under rather strict assumptions on the underlying risk measure. Therefore we
show, with a reformulated definition of suitability and in a slightly modified
setting, that there is a known suitable allocation principle that does not
require any properties of the underlying risk measure. Additionally we extend a
previous characterization result from the literature from a mean-risk to a
reward-risk setting. Formulations of this theory are also possible in a game
theoretic setting
Highly accurate numerical computation of implicitly defined volumes using the Laplace-Beltrami operator
This paper introduces a novel method for the efficient and accurate
computation of the volume of a domain whose boundary is given by an orientable
hypersurface which is implicitly given as the iso-contour of a sufficiently
smooth level-set function. After spatial discretization, local approximation of
the hypersurface and application of the Gaussian divergence theorem, the volume
integrals are transformed to surface integrals. Application of the surface
divergence theorem allows for a further reduction to line integrals which are
advantageous for numerical quadrature. We discuss the theoretical foundations
and provide details of the numerical algorithm. Finally, we present numerical
results for convex and non-convex hypersurfaces embedded in cuboidal domains,
showing both high accuracy and thrid- to fourth-order convergence in space.Comment: 25 pages, 17 figures, 3 table
Anal canal development in the embryonic and early foetal period
The aim of study is to investigate the development of the anal canal in human embryos and foetuses. In embryos at stage 19 the boundary between the ectodermal and endodermal linings of the anal canal is located just below the level of the internal anal sphincter muscle. Histological sections showed that the first signs of anal columns are observed in embryos at stage 21 (51 days)
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