375 research outputs found
On the level-slope-curvature effect in yield curves and eventual total positivity
Principal components analysis has become widely used in a variety of fields. In finance and, more specifically, in the theory of interest rate derivative modeling, its use has been pioneered by Litterman and Scheinkman [J. Fixed Income, 1 (1991), pp. 54--61]. Their key finding was that a few components explain most of the variance of treasury zero-coupon rates and that the first three eigenvectors represent level, slope, and curvature (LSC) changes on the curve. This result has been, since then, observed in various markets. Over the years, there have been several attempts at modeling correlation matrices displaying the observed effects as well as trying to understand what properties of those matrices are responsible for them. Using recent results of the theory of total positiveness [O. Kushel, Matrices with Totally Positive Powers and Their Generalizations, 2014], we characterize these matrices and, as an application, we shed light on the critique to the methodology raised by Lekkos [J. Derivatives, 8 (2000), pp. 72--83].Fil: Forzani, Liliana Maria. Consejo Nacional de Investigaciones CientĂficas y TĂ©cnicas. Centro CientĂfico TecnolĂłgico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; ArgentinaFil: Tolmasky, Carlos F.. University of Minnesota; Estados Unido
Evolution of complexity following a quantum quench in free field theory
Using a recent proposal of circuit complexity in quantum field theories
introduced by Jefferson and Myers, we compute the time evolution of the
complexity following a smooth mass quench characterized by a time scale in a free scalar field theory. We show that the dynamics has two distinct
phases, namely an early regime of approximately linear evolution followed by a
saturation phase characterized by oscillations around a mean value. The
behavior is similar to previous conjectures for the complexity growth in
chaotic and holographic systems, although here we have found that the
complexity may grow or decrease depending on whether the quench increases or
decreases the mass, and also that the time scale for saturation of the
complexity is of order (not parametrically larger).Comment: V2: added references, new plots, and improved discussion of results
on Section 5, V3: Few minor corrections. Published versio
Testing Lorentz invariance of dark matter
We study the possibility to constrain deviations from Lorentz invariance in
dark matter (DM) with cosmological observations. Breaking of Lorentz invariance
generically introduces new light gravitational degrees of freedom, which we
represent through a dynamical timelike vector field. If DM does not obey
Lorentz invariance, it couples to this vector field. We find that this coupling
affects the inertial mass of small DM halos which no longer satisfy the
equivalence principle. For large enough lumps of DM we identify a (chameleon)
mechanism that restores the inertial mass to its standard value. As a
consequence, the dynamics of gravitational clustering are modified. Two
prominent effects are a scale dependent enhancement in the growth of large
scale structure and a scale dependent bias between DM and baryon density
perturbations. The comparison with the measured linear matter power spectrum in
principle allows to bound the departure from Lorentz invariance of DM at the
per cent level.Comment: 42 pages, 9 figure
Structure and Identification of GARCH models
In questa tesi si studia la struttura e l'identificazione di modelli GARCH. Inoltre, verranno studiati modelli garch in forma di stato (SSGARCH) e modelli lineari gaussiani con errori GARCH. Vengono esposti i metodi di identificazione utilizzati come il metodo QMLE e l'algoritmo EM per i modelli in spazio di stato. Infine, vengono prodotte delle simulazioni per verificare il comportamento dei metodi di stima e della capacitĂ di stima e predizione della volatilitĂ dei modelli vist
Multi-scale active shape description in medical imaging
Shape description in medical imaging has become an increasingly important research field in recent years. Fast and high-resolution image acquisition methods like Magnetic Resonance (MR) imaging produce very detailed cross-sectional images of the human body - shape description is then a post-processing operation which abstracts quantitative descriptions of anatomically relevant object shapes. This task is usually performed by clinicians and other experts by first segmenting the shapes of interest, and then making volumetric and other quantitative measurements. High demand on expert time and inter- and intra-observer variability impose a clinical need of automating this process. Furthermore, recent studies in clinical neurology on the correspondence between disease status and degree of shape deformations necessitate the use of more sophisticated, higher-level shape description techniques. In this work a new hierarchical tool for shape description has been developed, combining two recently developed and powerful techniques in image processing: differential invariants in scale-space, and active contour models. This tool enables quantitative and qualitative shape studies at multiple levels of image detail, exploring the extra image scale degree of freedom. Using scale-space continuity, the global object shape can be detected at a coarse level of image detail, and finer shape characteristics can be found at higher levels of detail or scales. New methods for active shape evolution and focusing have been developed for the extraction of shapes at a large set of scales using an active contour model whose energy function is regularized with respect to scale and geometric differential image invariants. The resulting set of shapes is formulated as a multiscale shape stack which is analysed and described for each scale level with a large set of shape descriptors to obtain and analyse shape changes across scales. This shape stack leads naturally to several questions in regard to variable sampling and appropriate levels of detail to investigate an image. The relationship between active contour sampling precision and scale-space is addressed. After a thorough review of modem shape description, multi-scale image processing and active contour model techniques, the novel framework for multi-scale active shape description is presented and tested on synthetic images and medical images. An interesting result is the recovery of the fractal dimension of a known fractal boundary using this framework. Medical applications addressed are grey-matter deformations occurring for patients with epilepsy, spinal cord atrophy for patients with Multiple Sclerosis, and cortical impairment for neonates. Extensions to non-linear scale-spaces, comparisons to binary curve and curvature evolution schemes as well as other hierarchical shape descriptors are discussed
Born-Infeld inspired modifications of gravity
General Relativity has shown an outstanding observational success in the
scales where it has been directly tested. However, modifications have been
intensively explored in the regimes where it seems either incomplete or signals
its own limit of validity. In particular, the breakdown of unitarity near the
Planck scale strongly suggests that General Relativity needs to be modified at
high energies and quantum gravity effects are expected to be important. This is
related to the existence of spacetime singularities when the solutions of
General Relativity are extrapolated to regimes where curvatures are large. In
this sense, Born-Infeld inspired modifications of gravity have shown an
extraordinary ability to regularise the gravitational dynamics, leading to
non-singular cosmologies and regular black hole spacetimes in a very robust
manner and without resorting to quantum gravity effects. This has boosted the
interest in these theories in applications to stellar structure, compact
objects, inflationary scenarios, cosmological singularities, and black hole and
wormhole physics, among others. We review the motivations, various
formulations, and main results achieved within these theories, including their
observational viability, and provide an overview of current open problems and
future research opportunities.Comment: 212 pages, Review under press at Physics Report
Pricing swing options and other electricity derivatives
The deregulation of regional electricity markets has led to more competitive prices but also higher uncertainty in the future electricity price development. Most markets exhibit high volatilities and occasional distinctive price spikes, which results in demand for derivative products which protect the holder against high prices.
A good understanding of the stochastic price dynamics is required for the purposes of risk management and pricing derivatives. In this thesis we examine a simple spot price model which is the exponential of the sum of an Ornstein-Uhlenbeck and an independent pure jump process. We derive the moment generating function as well as various approximations to the probability density function of the logarithm of this spot price process at maturity T. With some restrictions on the set of possible martingale measures we show that the risk neutral dynamics remains within the class of considered models and hence we are able to calibrate the model to the observed forward curve and present semi-analytic formulas for premia of path-independent
options as well as approximations to call and put options on forward contracts with and without a delivery period. In order to price path-dependent options with multiple exercise rights like swing contracts a grid method is utilised which in turn uses approximations to the conditional density of the spot process.
Further contributions of this thesis include a short discussion of interpolation methods to generate a continuous forward curve based on the forward contracts with delivery periods observed in the market, and an investigation into optimal martingale measures in incomplete markets. In particular we present known results of q-optimal martingale measures in the setting of a stochastic volatility model and give a first indication of how to determine the q-optimal measure for q=0 in an exponential Ornstein-Uhlenbeck model consistent with a given forward curve
Quantum Deconstruction of 5D SQCD
We deconstruct the fifth dimension of 5D SCQD with general numbers of colors
and flavors and general 5D Chern-Simons level; the latter is adjusted by adding
extra quarks to the 4D quiver. We use deconstruction as a non-stringy UV
completion of the quantum 5D theory; to prove its usefulness, we compute
quantum corrections to the SQCD_5 prepotential. We also explore the
moduli/parameter space of the deconstructed SQCD_5 and show that for |K_CS| <
N_F/2 it continues to negative values of 1/(g_5)^2. In many cases there are
flop transitions connecting SQCD_5 to exotic 5D theories such as E0, and we
present several examples of such transitions. We compare deconstruction to
brane-web engineering of the same SQCD_5 and show that the phase diagram is the
same in both cases; indeed, the two UV completions are in the same universality
class, although they are not dual to each other. Hence, the phase structure of
an SQCD_5 (and presumably any other 5D gauge theory) is inherently
five-dimensional and does not depends on a UV completion.Comment: LaTeX+PStricks, 108 pages, 41 colored figures. Please print in colo
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