Distribución hiperbólica generalizada: una aplicación en la selección de portafolios y en la cuantificación de medidas de riesgo de mercado

En este trabajo se implementa una metodología para incluir momentos de orden superior en la selección de portafolios, haciendo uso de la Distribución Hiperbólica Generalizada, para posteriormente hacer un análisis comparativo frente al modelo de Markowitz.

Option pricing in market models driven by telegraph processes with jumps

Esta tesis está dividida en dos partes: en la primera parte se presentan y estudian los procesos telegráficos, los procesos de Poisson con compensador telegráfico y los procesos telegráficos con saltos. El estudio presentado en esta primera parte incluye el cálculo de las distribuciones de cada proceso, las medias y varianzas, así como las funciones generadoras de momentos entre otras propiedades. Utilizando estas propiedades en la segunda parte se estudian los modelos de valoración de opciones basados en procesos telegráficos con saltos. En esta parte se da una descripción de cómo calcular las medidas neutrales al riesgo, se encuentra la condición de no arbitraje en este tipo de modelos y por último se calcula el precio de las opciones Europeas de compra y venta.

Characterization and mechanism of action of the biological control agent Pantoea agglomerans EPS125

La soca EPS125 ha mostrat ser un efectiu agent de control biològic de diferents patògens fúngics de postcollita en diferents fruits. Degut a la seva elevada eficàcia, es va plantejar desenvolupar aquesta soca comercialment i per aquest motiu en el present treball es plantejà complementar la informació necessària pel seu registre. D'acord amb els resultats obtinguts mitjançant proves fenotípiques i genotípiques, la soca EPS125 queda inclosa dins l'espècie Pantoea agglomerans (Enterobacter agglomerans-Erwinia herbicola). En relació a la utilització de fonts de carboni, en el perfil i contingut d'àcids grassos cel·lulars i en el polimorfisme en la longitud dels fragments de macrorestricció genòmica (MRFLP), la soca EPS125 mostrà trets característics que la diferencien d'altres soques. Els dos marcadors moleculars (125.2 i 125.3) específics per la soca EPS125 dissenyats en el present treball mostraren ser semiespecífics per la seva detecció mitjançant la tècnica PCR i Real Time PCR. Quedant pendent l'anàlisi d'especificitat de l'ús combinat dels dos marcadors moleculars en una reacció PCR multiplex. P. agglomerans EPS125 ha mostrat ser molt efectiva en el control de Penicillium expansum en poma amb una dosi efectiva mitjana de 2.7x105 a 7x105 ufc/ml, i una ratio de 25-101 cèl·lules de la soca EPS125 per inactivar una espora del patogen segons el model de saturació hiperbòlica. Segons les aproximacions fenotípiques i estudis genotípics realitzats, sembla que els mecanismes de biocontrol utilitzats per la soca EPS125 contra P. expansum en poma estan directament relacionats amb la capacitat de formació de biofilm per aquesta soca.

Droplet shape of an anisotropic liquid

We investigate how a droplet of a complex liquid is modified by its internal nanoscale structure. As the liquid passes from an isotropic disordered state to an anisotropic layered morphology, the droplet shape switches from a smooth spherical cap to a terraced hyperbolic profile, which can be modeled as a stack of thin concentric circular disks with a repulsion between adjacent disk edges. Our ability to resolve the detailed shape of these defect-free droplets offers a unique opportunity to explore the underlying physics.

Moving boundary value problems for the wave equation

We study certain boundary value problems for the one-dimensional wave equation posed in a time-dependent domain. The approach we propose is based on a general transform method for solving boundary value problems for integrable nonlinear PDE in two variables, that has been applied extensively to the study of linear parabolic and elliptic equations. Here we analyse the wave equation as a simple illustrative example to discuss the particular features of this method in the context of linear hyperbolic PDEs, which have not been studied before in this framework.

Contextual emergence of mental states from neurodynamics

The emergence of mental states from neural states by partitioning the neural phase space is analyzed in terms of symbolic dynamics. Well-defined mental states provide contexts inducing a criterion of structural stability for the neurodynamics that can be implemented by particular partitions. This leads to distinguished subshifts of finite type that are either cyclic or irreducible. Cyclic shifts correspond to asymptotically stable fixed points or limit tori whereas irreducible shifts are obtained from generating partitions of mixing hyperbolic systems. These stability criteria are applied to the discussion of neural correlates of consiousness, to the definition of macroscopic neural states, and to aspects of the symbol grounding problem. In particular, it is shown that compatible mental descriptions, topologically equivalent to the neurodynamical description, emerge if the partition of the neural phase space is generating. If this is not the case, mental descriptions are incompatible or complementary. Consequences of this result for an integration or unification of cognitive science or psychology, respectively, will be indicated.

Optimal hedging with higher moments

This study proposes a utility-based framework for the determination of optimal hedge ratios (OHRs) that can allow for the impact of higher moments on hedging decisions. We examine the entire hyperbolic absolute risk aversion family of utilities which include quadratic, logarithmic, power, and exponential utility functions. We find that for both moderate and large spot (commodity) exposures, the performance of out-of-sample hedges constructed allowing for nonzero higher moments is better than the performance of the simpler OLS hedge ratio. The picture is, however, not uniform throughout our seven spot commodities as there is one instance (cotton) for which the modeling of higher moments decreases welfare out-of-sample relative to the simpler OLS. We support our empirical findings by a theoretical analysis of optimal hedging decisions and we uncover a novel link between OHRs and the minimax hedge ratio, that is the ratio which minimizes the largest loss of the hedged position. © 2011 Wiley Periodicals, Inc. Jrl Fut Mark

Symmetry breaking, mixing, instability, and low frequency variability in a minimal Lorenz-like system

Starting from the classical Saltzman two-dimensional convection equations, we derive via a severe spectral truncation a minimal 10 ODE system which includes the thermal effect of viscous dissipation. Neglecting this process leads to a dynamical system which includes a decoupled generalized Lorenz system. The consideration of this process breaks an important symmetry and couples the dynamics of fast and slow variables, with the ensuing modifications to the structural properties of the attractor and of the spectral features. When the relevant nondimensional number (Eckert number Ec) is different from zero, an additional time scale of O(Ec−1) is introduced in the system, as shown with standard multiscale analysis and made clear by several numerical evidences. Moreover, the system is ergodic and hyperbolic, the slow variables feature long-term memory with 1/f3/2 power spectra, and the fast variables feature amplitude modulation. Increasing the strength of the thermal-viscous feedback has a stabilizing effect, as both the metric entropy and the Kaplan-Yorke attractor dimension decrease monotonically with Ec. The analyzed system features very rich dynamics: it overcomes some of the limitations of the Lorenz system and might have prototypical value in relevant processes in complex systems dynamics, such as the interaction between slow and fast variables, the presence of long-term memory, and the associated extreme value statistics. This analysis shows how neglecting the coupling of slow and fast variables only on the basis of scale analysis can be catastrophic. In fact, this leads to spurious invariances that affect essential dynamical properties (ergodicity, hyperbolicity) and that cause the model losing ability in describing intrinsically multiscale processes.

Global responses of terrestrial productivity to contemporary climatic oscillations

The terrestrial biosphere is subjected to a wide range of natural climatic oscillations. Best known is the El Niño–southern oscillation (ENSO) that exerts globally extensive impacts on crops and natural vegetation. A 50-year time series of ENSO events has been analysed to determine those geographical areas that are reliably impacted by ENSO events. Most areas are impacted by changes in precipitation; however, the Pacific Northwest is warmed by El Niño events. Vegetation gross primary production (GPP) has been simulated for these areas, and tests well against independent satellite observations of the normalized difference vegetation index. Analyses of selected geographical areas indicate that changes in GPP often lead to significant changes in ecosystem structure and dynamics. The Pacific decadal oscillation (PDO) is another climatic oscillation that originates from the Pacific and exerts global impacts that are rather similar to ENSO events. However, the longer period of the PDO provided two phases in the time series with a cool phase from 1951 to 1976 and a warm phase from 1977 to 2002. It was notable that the cool phase of the PDO acted additively with cool ENSO phases to exacerbate drought in the earlier period for the southwest USA. By contrast in India, the cool phase of the PDO appears to reduce the negative impacts of warm ENSO events on crop production.

Acidity controls on dissolved organic carbon mobility in organic soils

Dissolved organic carbon (DOC) concentrations in surface waters have increased across much of Europe and North America, with implications for the terrestrial carbon balance, aquatic ecosystem functioning, water treatment costs and human health. Over the past decade, many hypotheses have been put forward to explain this phenomenon, from changing climate and land-management to eutrophication and acid deposition. Resolution of this debate has been hindered by a reliance on correlative analyses of time-series data, and a lack of robust experimental testing of proposed mechanisms. In a four-year, four-site replicated field experiment involving both acidifying and de-acidifying treatments, we tested the hypothesis that DOC leaching was previously suppressed by high levels of soil acidity in peat and organo-mineral soils, and therefore that observed DOC increases a consequence of decreasing soil acidity. We observed a consistent, positive relationship between DOC and acidity change at all sites. Responses were described by similar hyperbolic relationships between standardised changes in DOC and hydrogen ion concentrations at all sites, suggesting potentially general applicability. These relationships explained a substantial proportion of observed changes in peak DOC concentrations in nearby monitoring streams, and application to a UK-wide upland soil pH dataset suggests that recovery from acidification alone could have led to soil solution DOC increases in the range 46-126% by habitat type since 1978. Our findings raise the possibility that changing soil acidity may have wider impacts on ecosystem carbon balances. Decreasing sulphur deposition may be accelerating terrestrial carbon loss, and returning surface waters to a natural, high-DOC condition.

On the strong uniqueness of some finite dimensional Dirichlet operators

We prove essential self-adjointness of a class of Dirichlet operators in ℝn using the hyperbolic equation approach. This method allows one to prove essential self-adjointness under minimal conditions on the logarithmic derivative of the density and a condition of Muckenhoupt type on the density itself.

Toeplitz operators with distributional symbols on Bergman spaces

We study the boundedness and compactness of Toeplitz operators Ta on Bergman spaces , 1 < p < ∞. The novelty is that we allow distributional symbols. It turns out that the belonging of the symbol to a weighted Sobolev space of negative order is sufficient for the boundedness of Ta. We show the natural relation of the hyperbolic geometry of the disc and the order of the distribution. A corresponding sufficient condition for the compactness is also derived.

Toeplitz operators on Bergman spaces with locally integrable symbols

We study the boundedness of Toeplitz operators $T_a$ with locally integrable symbols on Bergman spaces $A^p(\mathbb{D})$, $1 < p < \infty$. Our main result gives a sufficient condition for the boundedness of $T_a$ in terms of some ``averages'' (related to hyperbolic rectangles) of its symbol. If the averages satisfy an ${o}$-type condition on the boundary of $\mathbb{D}$, we show that the corresponding Toeplitz operator is compact on $A^p$. Both conditions coincide with the known necessary conditions in the case of nonnegative symbols and $p=2$. We also show that Toeplitz operators with symbols of vanishing mean oscillation are Fredholm on $A^p$ provided that the averages are bounded away from zero, and derive an index formula for these operators.

Decadal to multidecadal variability and the climate change background

Three prominent quasi-global patterns of variability and change are observed using the Met Office's sea surface temperature (SST) analysis and almost independent night marine air temperature analysis. The first is a global warming signal that is very highly correlated with global mean SST. The second is a decadal to multidecadal fluctuation with some geographical similarity to the El Niño–Southern Oscillation (ENSO). It is associated with the Pacific Decadal Oscillation (PDO), and its Pacific-wide manifestation has been termed the Interdecadal Pacific Oscillation (IPO). We present model investigations of the relationship between the IPO and ENSO. The third mode is an interhemispheric variation on multidecadal timescales which, in view of climate model experiments, is likely to be at least partly due to natural variations in the thermohaline circulation. Observed climatic impacts of this mode also appear in model simulations. Smaller-scale, regional atmospheric phenomena also affect climate on decadal to interdecadal timescales. We concentrate on one such mode, the winter North Atlantic Oscillation (NAO). This shows strong decadal to interdecadal variability and a correspondingly strong influence on surface climate variability which is largely additional to the effects of recent regional anthropogenic climate change. The winter NAO is likely influenced by both SST forcing and stratospheric variability. A full understanding of decadal changes in the NAO and European winter climate may require a detailed representation of the stratosphere that is hitherto missing in the major climate models used to study climate change.

Rigid body trajectories in different 6D spaces

The objective of this paper is to show that the group SE(3) with an imposed Lie-Poisson structure can be used to determine the trajectory in a spatial frame of a rigid body in Euclidean space. Identical results for the trajectory are obtained in spherical and hyperbolic space by scaling the linear displacements appropriately since the influence of the moments of inertia on the trajectories tends to zero as the scaling factor increases. The semidirect product of the linear and rotational motions gives the trajectory from a body frame perspective. It is shown that this cannot be used to determine the trajectory in the spatial frame. The body frame trajectory is thus independent of the velocity coupling. In addition, it is shown that the analysis can be greatly simplified by aligning the axes of the spatial frame with the axis of symmetry which is unchanging for a natural system with no forces and rotation about an axis of symmetry.