A few more moments to finance theory: introducing higher moments in investment theory and econometrics

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Introducing higher moments in the CAPM: some basic ideas

We show how to include in the CAPM moments of any order, extending the mean-variance or mean-variance-skewness versions available until now. Then, we present a simple way to modify the formulae, in order to avoid the appearance of utility parameters. The results can be easily applied to practical portfolio design, with econometric inference and testing based on generalised method of moments procedures. An empirical application to the Brazilian stock market is discussed.

A CAPM with higher moments: theory and econometrics

We develop portfolio choice theory taking into consideration the first p~ moments of the underIying assets distribution. A rigorous characterization of the opportunity set and of the efficient portfolios frontier is given, as well as of the solutions to the problem with a general utility function and short sales allowed. The extension of c1assical meanvariance properties, like two-fund separation, is also investigated. A general CAPM is derived, based on the theoretical foundations built, and its empirical consequences and testing are discussed

On certain geometric aspects of portfolio optimisation with higher moments

We discuss geometric properties related to the minimisation of a portfolio kurtosis given its first two odd moments, considering a risk-less asset and allowing for short sales. The findings are generalised for the minimisation of any given even portfolio moment with fixed excess return and skewness, and then for the case in which only excess return is constrained. An example with two risky assets provides a better insight on the problems related to the solutions. The importance of the geometric properties and their use in the higher moments portfolio choice context is highlighted.

Finding a maximum skewness portfolio - A general solution to three-moments portfolio choice

Considering the three first moments and allowing short sales, the efficient portfolios set for n risky assets and a riskless one is found, supposing that agents like odd moments and dislike even ones. Analytical formulas for the solution surface are obtained and important geometric properties provide insights on its shape in the three dimensional space defined by the moments. A special duality result is needed and proved. The methodology is general, comprising situations in which, for instance, the investor trades a negative skewness for a higher expected return. Computation of the optimum portfolio weights is feasible in most cases.

Kondo-attractive-Hubbard model for the ordering of local magnetic moments in superconductors

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Repair Welding Effects on the Bending Fatigue Strength of AISI 4130 Aeronautical Steel used in a Critical to the Flight-Safety Structure

The aim of this study was to analyze the effect of successive TIG (tungsten inert gas) welding repairs on the reverse bending fatigue strength of AISI 4130 steel, which is widely used in components critical to the flight-safety. In order to simulate the abrupt maneuvers, wind bursts, motor vibration and helixes efforts, which generate cyclic bending loadings at the welded joints of a specific aircraft component called motor cradle, experimental reverse bending fatigue tests were carried out on specimens made from hot-rolled steel plate, 1.10 mm (0.043 in) thick, by mean of a SCHENK PWS equipment, with load ratio R = -1, under constant amplitude, at 30 Hz frequency and room temperature. It was observed that the bending fatigue strength decreases after the TIG (Tungsten Inert Gas) welding process application on AISI 4130 steel, with subsequent decrease due to re-welding sequence as well. Microstructural analyses and microhardness measurements on the base material, heat-affected zone (HAZ) and weld metal, as well as the effects of the weld bead geometry on the obtained results, have complemented this study.

BEM Formulations Based on Kirchhoff's Hypoyhesis to Perform Linear Bending Analysis of Plates Reinforced by Beams

In this work, are discussed two formulations of the boundary element method - BEM to perform linear bending analysis of plates reinforced by beams. Both formulations are based on the Kirchhoffs hypothesis and they are obtained from the reciprocity theorem applied to zoned plates, where each sub-region defines a beam or a stab. In the first model the problem values are defined along the interfaces and the external boundary. Then, in order to reduce the number of degrees of freedom kinematics hypothesis are assumed along the beam cross section, leading to a second formulation where the collocation points are defined along the beam skeleton, instead of being placed on interfaces. on these formulations no approximation of the generalized forces along the interface is required. Moreover, compatibility and equilibrium conditions along the interface are automatically imposed by the integral equation. Thus, these formulations require less approximation and the total number of the degrees of freedom is reduced. In the numerical examples are discussed the differences between these two BEM formulations, comparing as well the results to a well-known finite element code.

Analysis of the Coupled Stretching-Bending Problem of Stiffened Plates by a BEM Formulation Based on Reissner's Hypothesis

In this work, the plate bending formulation of the boundary element method - BEM, based on the Reissner's hypothesis, is extended to the analysis of plates reinforced by beams taking into account the membrane effects. The formulation is derived by assuming a zoned body where each sub-region defines a beam or a slab and all of them are represented by a chosen reference surface. Equilibrium and compatibility conditions are automatically imposed by the integral equations, which treat this composed structure as a single body. In order to reduce the number of degrees of freedom, the problem values defined on the interfaces are written in terms of their values on the beam axis. Initially are derived separated equations for the bending and stretching problems, but in the final system of equations the two problems are coupled and can not be treated separately. Finally are presented some numerical examples whose analytical results are known to show the accuracy of the proposed model.

A BEM formulation for analysing the coupled stretching-bending problem of plates reinforced by rectangular beams with columns defined in the domain

In this work, a boundary element formulation to analyse plates reinforced by rectangular beams, with columns defined in the domain is proposed. The model is based on Kirchhoff hypothesis and the beams are not required to be displayed over the plate surface, therefore eccentricity effects are taken into account. The presented boundary element method formulation is derived by applying the reciprocity theorem to zoned plates, where beams are treated as thin sub-regions with larger rigidities. The integral representations derived for this complex structural element consider the bending and stretching effects of both structural elements working together. The standard equilibrium and compatibility conditions along interface are naturally imposed, being the bending tractions eliminated along interfaces. The in-plane tractions and the bending and in-plane displacements are approximated along the beam width, reducing the number of degrees of freedom. The columns are introduced into the formulation by considering domain points where tractions can be prescribed. Some examples are then shown to illustrate the accuracy of the formulation, comparing the obtained results with other numerical solutions.

On the stabilising effect of gyroscopic moments in an automotive turbocharger

Automotive turbochargers, which operate at very high speeds, exceeding 180,000 r/min, exhibit two strong sub-harmonic modes of vibrations due to oil-whirl instability. These are a conical mode and an in-phase whirl mode. The gyroscopic effects can be very important in such a rotor system. This article presents a theoretical investigation into these effects on the conical whirl instability of a turbocharger induced by the angular (tilting) motion of a rigid rotor. A simplified linear model is used to analyse the rotor-bearing system by investigating the effects of the gyroscopic moment on the internal moments. A gyroscopic coefficient, defined by the geometry of the rotor, is shown to govern the stability of the conical whirl motion. A threshold value of 1/2 is determined for this coefficient to suppress the conical whirl. This value remains unaffected if the rotor is asymmetric and is supported by floating ring bearings, which is the case in a practical turbocharger.

Large magnetic dipole moments for neutrinos with arbitrary non-calculable masses

We show that there is a general sort of neutrino effective interactions which allows, under certain conditions, to have relatively large magnetic dipole moments for neutrinos while keeping their masses non-calculable and arbitrarily small. The main ingredient of our mechanism for generating large magnetic moment to the neutrinos is the existence of a neutral scalar which has the only role to give mass to the neutrinos or the existence of flavor changing neutral currents in the neutrino sector. Although our approach is model independent, some models in which those interactions arise are commented.

Laguerre moments and generalized functions

Here we explore the link between the moments of the Laguerre polynomials or Laguerre moments and the generalized functions (as the Dirac delta-function and its derivatives), presenting several interesting relations. A useful application is related to a procedure for calculating mean values in quantum optics that makes use of the so-called quasi-probabilities. One of them, the P-distribution, can be represented by a sum over Laguerre moments when the electromagnetic field is in a photon-number state. Consequently, the P-distribution can be expressed in terms of Dirac delta-function and derivatives. More specifically, we found a direct relation between P-distributions and the Laguerre factorial moments.

Bending of light in the framework of R + R2 gravity

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Nucleon magnetic moments in light-front models with quark mass asymmetries

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)