Estimating value at risk with semiparametric support vector quantile regression

Value at Risk (VaR) has been used as an important tool to measure the market risk under normal market. Usually the VaR of log returns is calculated by assuming a normal distribution. However, log returns are frequently found not normally distributed. This paper proposes the estimation approach of VaR using semiparametric support vector quantile regression (SSVQR) models which are functions of the one-step-ahead volatility forecast and the length of the holding period, and can be used regardless of the distribution. We find that the proposed models perform better overall than the variance-covariance and linear quantile regression approaches for return data on S&P 500, NIKEI 225 and KOSPI 200 indices.     

Sparse Penalized Forward Selection for Support Vector Classification

We propose a new binary classification and variable selection technique especially designed for high-dimensional predictors. Among many predictors, typically, only a small fraction of them have significant impact on prediction. In such a situation, more interpretable models with better prediction accuracy can be obtained by variable selection along with classification. By adding an ?₁-type penalty to the loss function, common classification methods such as logistic regression or support vector machines (SVM) can perform variable selection. Existing penalized SVM methods all attempt to jointly solve all the parameters involved in the penalization problem altogether. When data dimension is very high, the joint optimization problem is very complex and involves a lot of memory allocation. In this article, we propose a new penalized forward search technique that can reduce high-dimensional optimization problems to one-dimensional optimization by iterating the selection steps. The new algorithm can be regarded as a forward selection version of the penalized SVM and its variants. The advantage of optimizing in one dimension is that the location of the optimum solution can be obtained with intelligent search by exploiting convexity and a piecewise linear or quadratic structure of the criterion function. In each step, the predictor that is most able to predict the outcome is chosen in the model. The search is then repeatedly used in an iterative fashion until convergence occurs. Comparison of our new classification rule with ?₁-SVM and other common methods show very promising performance, in that the proposed method leads to much leaner models without compromising misclassification rates, particularly for high-dimensional predictors.     

Axiomatizations of the core on the universal domain and other natural domains

We prove that the core on the set of all transferable utility games with players contained in a universe of at least five members can be axiomatized by the zero inessential game property, covariance under strategic equivalence, anonymity, boundedness, the weak reduced game property, the converse reduced game property, and the reconfirmation property. These properties also characterize the core on certain subsets of games, e.g., on the set of totally balanced games, on the set of balanced games, and on the set of superadditive games. Suitable extensions of these properties yield an axiomatization of the core on sets of nontransferable utility games. Received September 1999/Final version December 2000     

Hyponormality of Toeplitz Operators with Polynomial Symbols: An Extremal Case

If T_φ is a hyponormal Toeplitz operator with polynomial symbol φ = ḡ + f (f, g ∈ H^∞ (𝕋 )) such that g divides f, and if ψ := then where μ is the leading coefficient of ψ and 𝒵(ψ) denotes the set of zeros of ψ. In this paper we present a necessary and sufficient condition for T_φ to be hyponormal when φ enjoys an extremal case in the above inequality, that is, equality holds in the above inequality.     

Parallel Smoothed Aggregation Multilevel Schwarz Preconditioned Newton-Krylov Algorithms for Poisson-Boltzmann Problems

We study a multilevel Schwarz preconditioned Newton-Krylov algorithm to solve the Poisson-Boltzmann equation with applications in multi-particle colloidal simulation. The smoothed aggregation-type coarse mesh space is introduced in collaboration with the one-level Schwarz method as a composite preconditioner for accelerating the convergence of a Krylov subspace method for solving the Jacobian system at each Newton step. The important feature of the proposed solution algorithm is that the geometric mesh information needed for constructing the multilevel preconditioner is the same as the one-level Schwarz method on the fine mesh. Other components, such as the definition of the coarse mesh, all the mesh transfer operators, and the coarse mesh problem, are taken care of by the Trillinos/ML packages of the Sandia National Laboratories in the United States. After algorithmic parameter tuning, we show that the proposed smoothed aggregation multilevel Newton-Krylov-Schwarz (NKS) algorithm numerically outperforms than smoothed aggregation multigrid method and one-level version of the NKS algorithm with satisfactory parallel performances up to a few thousand cores. Besides, we investigate how the electrostatic forces between particles for the separation distance depend on the radius of spherical colloidal particles and valence ratios of cation and anion in a cubic system.     

The Recognition of Double Euler Trails in Series-Parallel Networks

Given a series-parallel network (network, for short)N, its dual networkN′ is given by interchanging the series connection and the parallel connection of networkN. We usually use a series-parallel graph to represent a network. LetG[N] andG[N′] be graph representations ofNandN′, respectively. A sequence of edgese₁, e₂,…,e_kis said to form a common trail on (G[N], G[N′]) if it is a trail on bothG[N] andG[N′]. If a common trail covers all of the edges inG[N] andG[N′], it is called adouble Euler trail.However, there are many different graph representations for a network. We say that a networkNhas a double Euler trail (DET) if there is a common Euler trail for someG[N] and someG[N′]. Finding a DET in a network is essential for optimizing the layout area of a complementary CMOS functional cell. Maziasz and Hayes (IEEE Trans. Computer-Aided Design9(1990), 708–719) gave a linear time algorithm for solving the layout problem in fixedG[N] andG[N′] and an exponential algorithm for finding the optimal cover in a network without fixing graph representations. In this paper, we study properties of subnetworks of a DET network. According to these properties, we propose an algorithm that automatically generates the rules for composition of trail cover classes. On the basis of these rules, a linear time algorithm for recognizing DET networks is presented. Furthermore, we also give a necessary and sufficient condition for the existence of a double Euler circuit in a network.     

Experimental and theoretical study of the nonlinear response of agiant magnetostrictive rod

In this paper, a magnetomechanical coupling constitutive relation of the giant magnetostrictive material was investigated experimentally and theoretically. A grain-oriented magnetostrictive rod of iron and rare earth was tested under a combined magnetomechanical loading. Two types of experimental curves were obtained, i.e., the magnetostrictive curve of the extensional strain vs the magnetic field, and the curve of the magnetic polarization intensity vs the pre-stress. A new theoretical constitutive model, based on the density of domain switching, is developed. Comparison of the theoretical predictions with the experimental results indicates that this model can capture the main characteristics of the magnetoelastic coupling deformation of a giant magnetostrictive rod. The project supported by the National Natural Science Foundation of China (10025209, 10132010, 10102007)     

On the Dynamical Rayleigh-Taylor Instability

The classical Rayleigh-Taylor instability is shown to be valid in a nonlinear dynamical sense for smooth density profiles. (Accepted September 23, 2002) Published online February 26, 2003 Communicated by Y. Brenier     

Non-linear constitutive relations for magnetostrictive materials

In this paper, non-linear deformation behavior of magnetostrictive materials is studied and three magnetoelastic coupling constitutive models are developed. The standard square (SS) constitutive model is developed by means of truncating the polynomial expansion of the Gibbs free energy. The hyperbolic tangent (HT) constitutive equations, which involve a hyperbolic tangent magnetic-field dependence, are proposed to model the magnetic-field-induced strain saturation of magnetostrictive materials in the region of intense magnetic fields. A new model based on density of domain switching (DDS) is established in terms of the basic truth that magnetic domain switching underlies magnetostrictive deformation. In this model, it is assumed that the relation between density of domain switching, defined by the quantity of magnetic domains switched by per unit magnetic field and magnetic field can be described by a density function with normal distribution. The moduli in these constitutive models can be determined by a material function that is proposed to describe the dependence of the peak piezomagnetic coefficient on the compressive pre-stress for one-dimensional cases based on the experimental results published. The accuracy of the non-linear constitutive relations is evaluated by comparing the theoretical values with experimental results of a Terfenol-D rod operated under both compressive pre-stress and bias magnetic field. Results indicate that the SS constitutive equations can accurately predict the experimental results under a low or moderate magnetic field while the HT model can, to some extent, reflect the trend of saturation of magnetostrictive strain under a high magnetic field. The model based on DDS, which is more effective in simulating the experimental curves, can capture the main characteristics of the mechanism of magnetoelastic coupling deformation of a Terfenol-D rod, such as the notable dependence of magnetoelastic response on external stress and the saturation of magnetostrictive strain under intense magnetic fields. In addition, the SS constitutive relation for a general three-dimensional problem is discussed and an approach to characterize the modulus tensors is proposed.     

Allylic interactions in organometallics: probing Electronic structure in (η5-C5H5)Fe(CO)2R,R = CH3, η1-C3H5, η1-C5H5.

The He(I) photoelectron spectra of (η⁵-C₅H₅)Fe(CO)₂R, where R = CH₃, η¹-C₃H₅ and η¹-C₅H₅, have been recorded. The lowest lying ion states result from ionization of molecular orbitals with large Fe 3d character; these move to lower anergy when R places double bonds in an allylic relationship to the metal atom. The cyclic voltammetric oxidation potential correlates well with the energies of the lowest ion states. A significant interaction between olefin π orbitals and the allylic metal center is proposed.