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Testing Downside Risk Efficiency Under Market Distress
In moments of distress downside risk measures like Lower Partial Moments (LPM) are more appropriate than the standard variance to characterize risk. The goal of this paper is to study how to compare portfolios in these situations. In order to do that we show the close connection between mean-risk effciency sets and stochastic dominance under distress episodes of the market, and use the latter property to propose a hypothesis test to discriminate between portfolios across risk aversion levels. Our novel family of test statistics for testing stochastic dominance under distress makes allowance for testing orders of dominance higher than zero, for general forms of dependence between portfolios and can be extended to residuals of regression models. These results are illustrated in the empirical application for data from US stocks. We show that mean-variance strategies are stochastically dominated by mean-risk efficient sets in episodes of financial distress
Introduction to Modified Gravity: From the Cosmic Speedup Problem to Quantum Gravity Phenomenology
These notes represent a summary of the introductory part of a course on
modified gravity delivered at several Spanish Universities (Granada, Valencia,
and Valladolid), at the University of Wisconsin-Milwaukee (WI, USA), and at the
Karl-Franzens Universitaet (Graz, Austria) during the period 2008-2011. We
begin with a discussion of the classical Newtonian framework and how special
relativity boosted the interest on new theories of gravity. Then we focus on
Nordstrom's scalar theories of gravity and their influence on Einstein's theory
of general relativity. We comment on the meaning of the Einstein equivalence
principle and its implications for the construction of alternative theories of
gravity. We present the cosmic speedup problem and how theories can be
constrained attending to their weak-field behavior. We conclude by showing that
Palatini f(R) and f(R,Q) theories can be used to address different aspects of
quantum gravity phenomenology and singularity problems.Comment: 34 pages, 2 figures. Chapter written for the book "Aspects of Today's
Cosmology", Edited by: Antonio Alfonso-Faus, InTech Publishing, Rijeka,
Croatia, (2011), ISBN 978-953-307-626-3. The properly formatted version (26
pages) can be freely downloaded from the publisher's websit
Cosmology in Palatini theories of gravity
We discuss recent results on the cosmology of extended theories of gravity
formulated in the Palatini approach, i.e., assuming that metric and connection
are independent fields. In particular, we focus on the attempts to explain the
cosmic speedup with f(R) theories and on models that avoid the big bang
singularity. The field equations for gravity Lagrangians of the form
f(g_{\mu\nu},{R^\alpha}_{\beta\mu\nu}) (including torsion) are explicitly
derived and discussed.Comment: 16 pages, no figures. Contribution to the Proceedings of Spanish
Relativity Meeting ERE2011, Madrid 29 August - 2 September 2011 . Plenary
tal
Re-examination of Polytropic Spheres in Palatini f(R) Gravity
We investigate spherically symmetric, static matter configurations with
polytropic equation of state for a class of f(R) models in Palatini formalism
and show that the surface singularities recently reported in the literature are
not physical in the case of Planck scale modified lagrangians. In such cases,
they are just an artifact of the idealized equation of state used. In fact, we
show that for the models f(R)=R\pm\lambda R^2, with \lambda on the order of the
Planck length squared, the presence of a single electron in the Universe would
be enough to cure all stellar singularities of this type. From our analysis it
also follows that the stellar structure derived from these lagrangians is
virtually undistinguishable from that corresponding to General Relativity. For
ultraviolet corrected models far from the Planck scale, however, the surface
singularities may indeed arise in the region of validity of the polytropic
equation of state. This fact can be used to place constraints on the parameters
of particular models
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