Modeling style rotation: switching and re-switching

The purpose of this paper is to investigate the dynamics and statistics of style rotation based on the Barberis-Shleifer model of style switching. Investors in stocks regard the forecasting of style-relative performance, especially style rotation, as highly desirable but difficult to achieve in practice. Whilst we do not claim to be able to do this in an empirical sense, we do provide a framework for addressing these issues. We develop some new results from the Barberis-Shleifer model which allows us to understand some of the time series properties of style relative price performance and determine the statistical properties of the time until a switch between styles. We apply our results to a set of empirical data to get estimates of some of the model parameters including the level of risk aversion of market participants

Transverse Spin Diffusion in a Dilute Spin-Polarized Degenerate Fermi Gas

We re-examine the calculation of the transverse spin-diffusion coefficient in a dilute degenerate spin-polarized Fermi gas, for the case of s-wave scattering. The special feature of this limit is that the dependence of the spin diffusion coefficient on temperature and field can be calculated explicitly with no further approximations. This exact solution uncovers a novel intermediate behavior between the high field spin-rotation dominated regime in which $D_{\bot} \propto H^{-2}$, $D_{\parallel} \propto T^{-2}$, and the low-field isotropic, collision dominated regime with $D_{\bot} = D_{\parallel} \propto T^{-2}$. In this intermediate regime, $D_{\bot ,\parallel} \propto T^{-2}$ but $D_{\bot} \neq D_{\parallel}$. We also present an analytical calculation of the self-energy in the s-wave approximation for a dilute spin-polarized Fermi gas, at zero temperature. This emphasizes the failure of the conventional Fermi-liquid phase space arguments for processes involving spin flips. We close by reviewing the evidence for the existence of the intermediate regime in experiments on weakly spin-polarized $^3{\rm He}$ and $^3{\rm He} - ^4{\rm He}$ mixtures.Comment: 38 pages, Latex-Revtex, 9 PostScript figures. Minor revisions, misprints corrected, references adde

Efficiency with Endogenous Population Growth

In this paper, we generalize the notion of Pareto-efficiency to make it applicable to environments with endogenous populations. Two different efficiency concepts are proposed, P-efficiency and A-efficiency. The two concepts differ in how they treat people that are not born. We show how these concepts relate to the notion of Pareto efficiency when fertility is exogenous. We then prove versions of the first welfare theorem assuming that decision making is efficient within the dynasty. Finally, we give two sets of sufficient conditions for non-cooperative equilibria of family decision problems to be efficient. These include the Barro and Becker model as a special casePareto efficiency, endogenous fertility, first welfare theorem

Efficiency with Endogenous Population Growth

In this paper, we generalize the notion of Pareto-efficiency to make it applicable to environments with endogenous populations. Two efficiency concepts are proposed, P-efficiency and A-efficiency. The two concepts differ in how they treat people who are not born. We show how these concepts relate to the notion of Pareto-efficiency when fertility is exogenous. We then prove versions of the first welfare theorem assuming that decision making is efficient within the dynasty. Finally, we give two sets of sufficient conditions for non-cooperative equilibria of family decision problems to be efficient. These include the Barro and Becker model as a special case.

Efficiency with endogenous population growth

In this paper, we generalize the notion of Pareto-efficiency to make it applicable to environments with endogenous populations. Two efficiency concepts are proposed, P-efficiency and A-efficiency. The two concepts differ in how they treat people who are not born. We show how these concepts relate to the notion of Pareto-efficiency when fertility is exogenous. We then prove versions of the first welfare theorem assuming that decision making is efficient within the dynasty. Finally, we give two sets of sufficient conditions for noncooperative equilibria of family decision problems to be efficient. These include the Barro and Becker model as a special case.Population

Efficiency with Endogenous Population Growth

In this paper, we generalize the notion of Pareto-efficiency to make it applicable to environments with endogenous populations. Two efficiency concepts are proposed, P-efficiency and A-efficiency. The two concepts differ in how they treat potential agents that are not born. We show that these concepts are closely related to the notion of Pareto-efficiency when fertility is exogenous. We then prove versions of the first welfare theorem assuming that decision making is efficient within the dynasty. We discuss two sets of sufficient conditions for noncooperative equilibria of family decision problems to be efficient. These include the Barro and Becker model as a special case. Finally, we study examples of equilibrium settings in which fertility decisions are not efficient, and classify them into ones where inefficiencies arise inside the family and ones where they arise across families.pareto optimality, first welfare theorem, fertility, dynasty, altruism

On Accuracy Order of Fourier Coefficients Computation for Periodic Signal Processing Models

The article is devoted to construction piecewise constant functions for modelling periodic signal. The aim of the paper is to suggest a way to avoid discontinuity at points where waveform values are obtained. One solution is to introduce shifted step function whose middle points within its partial intervals coincide with points of observation. This means that large oscillations of Fourier partial sums move to new jump discontinuities where waveform values are not obtained. Furthermore, any step function chosen to model periodic continuous waveform determines a way to calculate Fourier coefficients. In this case, the technique is certainly a weighted rectangular quadrature rule. Here, the weight is either unit or trigonometric. Another effect of the solution consists in following. The shifted function leads to application midpoint quadrature rules for computing Fourier coefficients. As a result the formula for zero coefficient transforms into trapezoid rule. In the same time, the formulas for other coefficients remain of rectangular type

Recoil corrections in the hydrogen isoelectronic sequence

A version of the Bethe-Salpeter equation appropriate for calculating recoil corrections in highly charged hydrogenlike ions is presented. The nucleus is treated as a scalar particle of charge Z, and the electron treated relativistically. The known recoil corrections of order $m^2/M(Z\alpha)^4$ are derived in both this formalism and in NRQED