不同模型下ES风险度量的计算

给出当金融资产遵从几何布朗运动时期望损失的计算。当金融资产价格的对数收益率服从均值方程为ARMA模型,方差方程为GARCH(s,n)模型,而均值修正后的收益率分别服从正态分布、t分布和GED分布时,给出了期望损失的计算。     

Radical scavenging efficiency of different fullerenes C60-C70 and fullerene soot

This investigation was undertaken to determine the antioxidant activity of a range of fullerenes C₆₀ and C₇₀ in order to rank them according to their comparative efficiency. The model reaction of initiated (2,2′- azobisisobutyronitrile, AIBN) cumene oxidation was used to determine rate constants for addition of radicals to fullerenes. Measurements of oxidation rates in the presence of different fullerenes showed that the antioxidant activity as well as the mechanism and mode of inhibition were different for fullerenes C₆₀ and C₇₀ and fullerene soot. All fullerenes - C₆₀ of gold grade, C₆₀/C₇₀ (93/7, mix 1), C₆₀/C₇₀ (80 ± 5/20 ± 5, mix 2) and C₇₀ operated as alkyl radical acceptora, whereas fullerene soot surprisingly retarded the model reaction by a dual mode similar to that for the fullerenes and with an induction period like many of the sterically hindered phenolic and amine antioxidants. For the C₆₀ and C₇₀ the oxidation rates were found to depend linearly on the reciprocal square root of the concentration over a sufficiently wide range thereby fitting the mechanism for the addition of cumylalkyl radicals to the fullerene core. This is consistent with literature data on the more ready and rapid addition of alkyl and alkoxy radicals to the fullerenes compared with peroxy radicals. Rate constants for the addition of cumyl radicals to the fullerenes were determined to be k_(333K) = (1.9 ± 0.2) × 10⁸ (C₆₀); (2.3 ± 0.2) × 10⁸ (C₆₀/C₇₀, mix 1); (2.7 ± 0.2) × 10⁸ (C₆₀/C₇₀, mix 2); (3.0 ± 0.3) × 10⁸ (C₇₀), M⁻¹ s⁻¹. The increasing C₇₀ constituent in the fullerenes leads to a corresponding increase in the rate constant.The fullerene soot inhibits the model reaction according to the mechanism of trapping of peroxy radicals; the oxidation proceeds with a pronounced induction period and kinetic curves are linear in semi-logarithmic coordinates.For the first time the effective concentration of inhibiting centres and inhibition rate constants for the fullerene soot have been determined to be fn[C₆₀−soot] = (2.0 ± 0.1) × 10⁻⁴ mol g⁻¹ and k_inh = (6.5 ± 1.5) × 10³ M⁻¹ s⁻¹ respectively.The kinetic data obtained specify the level of antioxidant activity for the commercial fullerenes and scope for their rational use in different composites. The results may be helpful for designing an optimal profile of composites containing fullerenes.     

Mechanistic investigation, kinetic modeling and analysis parameters of poly(3-hexylthiophene) degradation to fullerenes

Thermal degradation of Poly (3-hexylthiopene) (P3HT) was studied under nitrogen environment. Kinetic parameters of thermal degradation were determined using Vyazovkin model free method and model fitting method. Vyazovkin model free kinetic analysis is carried out to understand the variation of activation energy (E_α) required for degradation of polymer with conversion (α). Various reaction models have been tested for probable reaction mechanism using hybrid genetic algorithm (HGA). Diffusion model and nucleation & growth with n = 2/3 has prominent role in thermal decomposition of P3HT. A plausible degradation route is proposed based on the experimental details acquired from gas chromatography (GC), Raman spectroscopy, FTIR spectroscopy, powder X-ray diffractometry (XRD), scanning electron microscopy (SEM) and transmission electron microscopy (TEM). Degradation of P3HT starts at around 195 °C with release of lighter units like CS. Further increase in the temperature results in detachment of the hexyl chain from P3HT and the residue obtained at 1050 °C contains fullerenes mixed with amorphous carbon.     

An improved model averaging scheme for logistic regression

Recently, penalized regression methods have attracted much attention in the statistical literature. In this article, we argue that such methods can be improved for the purposes of prediction by utilizing model averaging ideas. We propose a new algorithm that combines penalized regression with model averaging for improved prediction. We also discuss the issue of model selection versus model averaging and propose a diagnostic based on the notion of generalized degrees of freedom. The proposed methods are studied using both simulated and real data.     

Asymptotic normality and confidence intervals for inverse regression models with convolution-type operators

We consider inverse regression models with convolution-type operators which mediate convolution on (d≥1) and prove a pointwise central limit theorem for spectral regularisation estimators which can be applied to construct pointwise confidence regions. Here, we cope with the unknown bias of such estimators by undersmoothing. Moreover, we prove consistency of the residual bootstrap in this setting and demonstrate the feasibility of the bootstrap confidence bands at moderate sample sizes in a simulation study.     

A symmetric inverse eigenvalue problem in structural dynamic model updating

In this paper, we first give the representation of the general solution of the following inverse eigenvalue problem (IEP): Given X∈R^n×p and a diagonal matrix Λ∈R^p×p, find real-valued symmetric (2r+1)-diagonal matrices M and K such that MXΛ=KX. We then consider an optimal approximation problem: Given real-valued symmetric (2r+1)-diagonal matrices M_a,K_a∈R^n×n, find such that where S_MK is the solution set of IEP. We show that the optimal approximation solution is unique and derive an explicit formula for it.     

Estimating copula densities, using model selection techniques

Recently a new way of modeling dependence has been introduced considering a sequence of parametric copula models, covering more and more dependency aspects and thus giving a closer approximation to the true copula density. The method uses contamination families based on Legendre polynomials. It has been shown that in general after a few steps accurate approximations are obtained. In this paper selection of the adequate number of steps is considered, and estimation of the unknown parameters within the chosen contamination family is established, thus obtaining an estimator of the unknown copula density. There should be a balance between the complexity of the model and the number of parameters to be estimated. High complexity gives a low model error, but a large stochastic or estimation error, while a very simple model gives a small stochastic error, but a large model error. Techniques from model selection are applied, thus letting the data tell us which aspects are important enough to capture into the model. Natural and simple estimators of the involved Fourier coefficients complete the procedure. Theoretical results show that the expected quadratic error is reduced by the selection rule to the same order of magnitude as in a classical parametric problem. The method is applied on a real data set, illustrating that the new method describes the data set very well: the error involved in the classical Gaussian copula density is reduced with no fewer than 50%.     

Estimating value at risk of portfolio by conditional copula-GARCH method

Copula functions represent a methodology that describes the dependence structure of a multi-dimension random variable and has become one of the most significant new tools to handle risk factors in finance, such as Value-at Risk (VaR), which is probably the most widely used risk measure in financial institutions. Combining copula and the forecast function of the GARCH model, this paper proposes a new method, called conditional copula-GARCH, to compute the VaR of portfolios. This work presents an application of the copula-GARCH model in the estimation of a portfolio’s VaR, composed of NASDAQ and TAIEX. The empirical results show that, compared with traditional methods, the copula model captures the VaR more successfully. In addition, the Student-t copula describes the dependence structure of the portfolio return series quite well.     

Analysis of vibrations in a nonhomogeneous thermoelastic thin annular disk under dynamic pressure

The forced vibration analysis of nonhomogeneous thermoelastic, isotropic, thin annular disk under periodic and exponential types of axisymmetric dynamic pressures applied on its inner boundary has been performed and analytical benchmark solution has been obtained. The material has been assumed to have inhomogeneity according to a simple power law in the radial coordinate. The present analysis has been worked out in the context of generalized theory of thermoelasticity with one relaxation time. The two coupled partial differential equations have been clubbed and solved by employing Laplace transform technique to obtain the solution for radial displacement and temperature change in the space domain. In order to obtain the solution in physical domain, the inversion of the transform has been carried out by using residue calculus. The radial displacement, radial stress, circumferential stress, and temperature change have been computed numerically for copper material annular disk. The numerically computed results have been presented graphically to demonstrate the effect of two different types of dynamic pressure in reference to homogeneous and nonhomogeneous material disk. The results for homogeneous material disk have been deduced and validated with that available in literature. The closed-form solution obtained here is interesting and allows further parametric studies of nonhomogeneous structures.     

An experimental study on the acoustic absorption of sand panels

Potentially sand panels could be used as novel sound absorbing materials that are fire resistant, environmentally friendly, mechanically strong and have good durability. However, the performance of sand panels as sound absorbers has not yet been studied. Results of measurements in a reverberation chamber of the random-incidence absorption coefficients of 13 different sand panel compositions and configurations with air gaps are reported. Also the flow resistivities and bulk densities have been measured. The results prove that sand panels could offer effective and wide-band acoustic absorption. As is the case with conventional sound absorbing materials, adding an air space is found to be the most effective way to widen the absorption bands and improve the overall absorption. Comparisons of the measured sand panel absorption data with predictions of the Delany and Bazley and Voronina models reveal that, while neither model is very accurate, the former gives more accurate predictions especially for sand panels with lower flow resistivity and smaller thickness.