Modeling Asset Prices

As an asset is traded, its varying prices trace out an interesting time series. The price, at least in a general way, reflects some underlying value of the asset. For most basic assets, realistic models of value must involve many variables relating not only to the individual asset, but also to the asset class, the industrial sector(s) of the asset, and both the local economy and the general global economic conditions. Rather than attempting to model the value, we will confine our interest to modeling the price. The underlying assumption is that the price at which an asset trades is a "fair market price" that reflects the actual value of the asset. Our initial interest is in models of the price of a basic asset, that is, not the price of a derivative asset. Usually instead of the price itself, we consider the relative change in price, that is, the rate of return, over some interval of time. The purpose of asset pricing models is not for prediction of future prices; rather the purpose is to provide a description of the stochastic behavior of prices. Models of price changes have a number of uses, including, for investors, optimal construction of portfolios of assets and, for market regulators, maintaining a fair and orderly market. A major motivation for developing models of price changes of given assets is to use those models to develop models of fair value of derivative assets that depend on the given assets.Discrete time series models, continuous time diffusion models, models with jumps, stochastic volatility, GARCH

How Computational Statistics Became the Backbone of Modern Data Science

This first chapter serves as an introduction and overview for a collection of articles surveying the current state of the science of computational statistics. Earlier versions of most of these articles appeared in the first edition of Handbook of Computational Statistics: Concepts and Methods, published in 2004. There have been advances in all of the areas of computational statistics, so we feel that it is time to revise and update this Handbook. This introduction is a revision of the introductory chapter of the first edition.Discrete time series models, continuous time diffusion models, models with jumps, stochastic volatility, GARCH

Apparent horizons in simplicial Brill wave initial data

We construct initial data for a particular class of Brill wave metrics using Regge calculus, and compare the results to a corresponding continuum solution, finding excellent agreement. We then search for trapped surfaces in both sets of initial data, and provide an independent verification of the existence of an apparent horizon once a critical gravitational wave amplitude is passed. Our estimate of this critical value, using both the Regge and continuum solutions, supports other recent findings.Comment: 7 pages, 6 EPS figures, LaTeX 2e. Submitted to Class. Quant. Gra

Exploring the Tensions in Organizational Theories

Today’s organizations cannot survive through the application of old theories which are considered obsolete. However, some of these ‘old theories’ still maintain their relevance in the operation of businesses today. The complexity and dynamism of the world have introduced more tensions in organizational theories as some of the theories were introduced with the intention of refuting existing theories. Each new theory had it own assumptions, characteristics and hypothetical beliefs which made them attract relevance when they were first introduced because they were assumed to fill an existing gap. This paper explores some of these theories and maintains that the tensions they create is borne out of the battle for superiority when non can actually solve all organizational problems

Rotating star initial data for a constrained scheme in numerical relativity

A new numerical code for computing stationary axisymmetric rapidly rotating stars in general relativity is presented. The formulation is based on a fully constrained-evolution scheme for 3+1 numerical relativity using the Dirac gauge and maximal slicing. We use both the polytropic and MIT bag model equations of state to demonstrate that the code can construct rapidly rotating neutron star and strange star models. We compare numerical models obtained by our code and a well-established code, which uses a different gauge condition, and show that the two codes agree to high accuracy.Comment: Minor changes and one figure added. Version accepted for publication in Class. Quant. Gra

Connected component identification and cluster update on GPU

Cluster identification tasks occur in a multitude of contexts in physics and engineering such as, for instance, cluster algorithms for simulating spin models, percolation simulations, segmentation problems in image processing, or network analysis. While it has been shown that graphics processing units (GPUs) can result in speedups of two to three orders of magnitude as compared to serial codes on CPUs for the case of local and thus naturally parallelized problems such as single-spin flip update simulations of spin models, the situation is considerably more complicated for the non-local problem of cluster or connected component identification. I discuss the suitability of different approaches of parallelization of cluster labeling and cluster update algorithms for calculations on GPU and compare to the performance of serial implementations.Comment: 15 pages, 14 figures, one table, submitted to PR

Investigation of Core Transport Barriers in DIII-D Discharges with off-axis Te Profile Peaks

DIII-D discharges that transition to H-mode solely with off-axis electron cyclotron heating (ECH) often exhibit strong off-axis peaking of electron temperature profiles at the heating location. Electron heat transport properties near these off-axis temperature peaks have been studied using modulated ECH. The Fourier analyzed electron temperature data have been used to infer electron thermal diffusivity. Comparisons with numerical solutions of the time-dependent electron thermal equation find that the data are consistent with a narrow region with electron diffusivity $\chi_e$ an order of magnitude lower than the average value across the plasma, suggesting an electron internal transport barrier (ITB) near the ECH heating location. Detailed profile analysis and equilibrium reconstructions suggest that the formation of these ITBs are correlated with off-axis values of the safety factor $q$ being near 1. Furthermore, the ECH driven H-mode discharges demonstrate more rapid electron heating rate near the ECH deposition location than L-mode discharges with higher auxiliary ECH heating power. Additional modeling attributes this difference to the modification of electron heat transport in the core at the L-H transition, which also sustains the off-axis electron temperature peaks

The constraints as evolution equations for numerical relativity

The Einstein equations have proven surprisingly difficult to solve numerically. A standard diagnostic of the problems which plague the field is the failure of computational schemes to satisfy the constraints, which are known to be mathematically conserved by the evolution equations. We describe a new approach to rewriting the constraints as first-order evolution equations, thereby guaranteeing that they are satisfied to a chosen accuracy by any discretization scheme. This introduces a set of four subsidiary constraints which are far simpler than the standard constraint equations, and which should be more easily conserved in computational applications. We explore the manner in which the momentum constraints are already incorporated in several existing formulations of the Einstein equations, and demonstrate the ease with which our new constraint-conserving approach can be incorporated into these schemes.Comment: 10 pages, updated to match published versio

Measuring degree-degree association in networks

The Pearson correlation coefficient is commonly used for quantifying the global level of degree-degree association in complex networks. Here, we use a probabilistic representation of the underlying network structure for assessing the applicability of different association measures to heavy-tailed degree distributions. Theoretical arguments together with our numerical study indicate that Pearson's coefficient often depends on the size of networks with equal association structure, impeding a systematic comparison of real-world networks. In contrast, Kendall-Gibbons' $\tau_{b}$ is a considerably more robust measure of the degree-degree association