Conditional VaR estimation using Pearson’s type IV distribution

This paper presents a new value at risk (VaR) estimation model for equity returns time series and tests it extensively on Stock Indices of 14 countries. Two most important stylized facts of such series are volatility clustering, and non-normality as a result of fat tails of the return distribution. While volatility clustering has been extensively studied using the GARCH model and its various extensions, the phenomenon of non-normality has not been comprehensively explored, at least in the context of VaR estimation. A combination of extreme value theory (EVT) and GARCH has been explored to analyze financial data showing non-normal behavior. This paper proposes a combination of the Pearson’s Type IV distribution and the GARCH (1, 1) approach to furnish a new method with superior predictive abilities. The approach is back tested for the entire sample as well as for a holdout sample using rolling windows.     

Facile preparation of monodisperse hollow cross‐linked chitosan microspheres

We have successfully prepared biocompatible and biodegradable hollow microspheres using carboxyl‐functionalized polystyrene particles as core template and the chitosan cross‐linked with glutaraldehyde as the shell. The monodisperse carboxyl‐functionalized polystyrene particles were made by emulsifier‐free emulsion polymerization. The structure, morphology, and constitution of the carboxyl‐functionalized polystyrene particles were characterized by FTIR, scanning electron microscopy (SEM), transmission electron microscopy (TEM), and X‐ray photoelectron spectroscopy (XPS). The structure, morphology, and formation process of the hollow cross‐linked chitosan microspheres were characterized by FTIR, SEM, and TEM. The results revealed that the latex particles were removed by exposed to solvent and the microspheres exhibited the hollow structure. This work confirmed that the hollow microspheres were accomplished by fabricating on the basis of chemical cross‐linking on the surface of the carboxyl‐functionalized polystyrene particles and then removing off the cores of particles. Moreover, with the increase of carboxyl‐functionalization degree at the surface of latexes and the increase of cross‐linking period, the thicker and firmer monodisperse hollow microspheres were obtained. In addition, a water‐soluble drug, salicylic acid, encapsulated in the microcapsules slowly released at pH 1.2. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 228–237, 2008     

Synthesis of self‐healing supramolecular rubbers from fatty acid derivatives,diethylene triamine,and urea

We describe the synthesis of supramolecular self‐healing elastomers from vegetable oil fatty acid derivatives, diethylene triamine, and urea. Our strategy to obtain materials that are self‐healing but do not flow relies on the use of a wide molecular distribution of randomly branched oligomers equipped with self‐complementary and complementary hydrogen bonding groups. We prepared such oligomers with a two steps procedure. In the first step, diethylene triamine was condensed with dimer acids. In the second step, the oligomers obtained were allowed to react with urea. The molecules were characterized by NMR and IR spectroscopies and Monte‐Carlo simulations were used to analyze the molecular size distribution. The sensitivity to small variations of the experimental conditions has been examined and the robustness of the synthetic procedure optimized. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 7925–7936, 2008     

Control of flow rate in supercritical fluid chromatography

Summary Supercritical Fluid Chromatograph was constructed using two pumps and two restrictors. With this system in conjunction with the fused silica column packed with relatively large particles (40 μm), the flow rate was controlled both for isobaric and pressure programmed operations. Application of this system to the determination of molecular weight distribution of polystyrene oligomers was presented.     

VALUE DISTRIBUTION THEORY AND DIOPHANTINE APPROXIMATION

In this paper, we will introduce some problems and results between Diophantine approximation and value distribution theory.     

社会分配的和谐结构

实现和谐社会需要一个与之相适应的社会分配结构.借助基尼系数描述了一种和谐的社会分配结构.通过观察和分析我国近年的经济数据可以发现,为实现和谐的分配状态,我们必须应对许多严峻挑战:城乡差别依旧过大;接近占总人口20%的最贫困人群几乎没有财富积累;过大的地下经济扭曲并影响了社会的公平分配.进行社会分配必须兼顾均衡与效率.要实现和谐的分配状态,可以有许多考虑和选择.建议采取法律、法规、科技、政策和行政的各种手段,要坚决消灭近20%最贫困人群的入不敷出的情形;要全力打造中等收入阶层;要加大取缔黑色收入规范灰色收入的力度;要加快城镇化建设的步伐;要积极营建促进全民创业的环境.     

Analysis of ordered categorical data from repeated measurements assuming a quantitative latent variable

Summary The purpose of the present paper is to propose an analytical method for ordered categorical responses obtained from a repeated measurement/longitudinal experiment. The ordered categorical scale is assumed to be a manifestation of a latent quantitative variable. A linear model is assumed for location parameters of the underlying distributions. Weighted least square method is applied to parameter estimation and subsequent analysis. Two data sets are analyzed to show several aspects of analysis by the proposed model and to discuss comparative characteristics of analysis compared with earlier analysis. A mention is made for a computer software program for the proposed model.     

Asymptotic distribution of the increase of the largest canonical correlation when one of the vectors is augmented

Let r₁ > r₂ > … be the sample canonical correlations in a sample of size n from a multivariate normal population partitioned into two subvectors with population canonical correlations ₁ > ₂ > …. Let one of the subvectors be augmented by adding one or more variables to it. For the increase in the largest canonical correlation, Δr in the sample and Δ in the population, it is shown that √n(Δr − Δ) → ^DN(0, σ²) and a formula for σ² is derived.     

An analytical solution for the model of drug distribution and absorption in small intestine

According to the physiological and anatomical characteristics of small intestine, neglecting the effect of its motility on the distribution and absorption of drug and nutrient, Y. Miyamoto et al.^[1] proposed a model of two-dimensional laminar flow in a circular porous tube with permeable wall and calculated the concentration profile of drug by numerical analysis. In this paper, we give a steady state analytical solution of the above model including deactivation term. The obtained results are in agreement with the results of their numerical analysis. Moreover the analytical solution presented in this paper reveals the relation among the physiological parameters of the model and describes the basic absorption rule of drug and nutrient through the intestinal wall and hence provides a theoretical basis for determining the permeability and reflection coefficient through in situ experiments. The project supported by NSF of Shandong Province     

Some inverse problems in rheology leading to integral equations

Two inverse problems of the integral type, which are of the general importance to rheology, are discussed. The first of them is the possibility of calculating the molecular weight distribution (MWD) from the flow curve and the second one is the interrelation between creep and relaxation functions. It was shown that the first problem is incorrect and any solution is unstable in respect to minor experimental errors. It means that the general solution of this problem is impossible in principle and only estimations of the width of unimodal MWD can be received from the curvature of the flow curve. The possibility of the correct calculation of the creep function exists in case the relaxation curve being approximated by the sum of exponential members. But the approximation of the relaxation curve within the experimental accuracy is the necessary, but not sufficient condition for the correct solution of this integral inverse problem, because not every mode of approximation leads to the satisfactory prediction of creep function.Delivered as the Courtaulds Lecture at the Golden Jubilee Conference of the British Society of Rheology and Third European Rheology Conference, Edinburgh, 3–7 September, 1990.