Individual loss reserving using paid–incurred data

This paper develops a stochastic model for individual claims reserving using observed data on claim payments as well as incurred losses. We extend the approach of Pigeon et al. (2013), designed for payments only, towards the inclusion of incurred losses. We call the new technique the individual Paid and Incurred Chain (iPIC) reserving method. Analytic expressions are derived for the expected ultimate losses, given observed development patterns. The usefulness of this new model is illustrated with a portfolio of general liability insurance policies. For the case study developed in this paper, detailed comparisons with existing approaches reveal that iPIC method performs well and produces more accurate predictions.     

多元统计分析方法在大鼠肾病疗效分析中的应用

本文根据河北医科大学运用中药青风藤提取物青藤碱治疗患系膜增生性肾小球肾炎的SD大鼠的最新实验数据,采用多元统计分析的Fisher判别法,对该实验制模过程、治疗效果进行判别分析.从统计意义上讲,该实验制模是成功的,青藤碱的治疗效果与常用药物雷公藤多苷一样比较显著.     

Determination of intrinsic viscosity of poly(ethylene terephthalate) using infrared spectroscopy and multivariate calibration method

A methodology was developed to determine the intrinsic viscosity of poly(ethylene terephthalate) (PET) using diffuse reflectance infrared Fourier transform spectroscopy (DRIFTS) and multivariate calibration (MVC) methods. Multivariate partial least squares calibration was applied to the spectra using mean centering and cross validation. The results were correlated to the intrinsic viscosities determined by the standard chemical method (ASTM D 4603-01) and a very good correlation for values in the range from 0.346 to 0.780 dL g⁻¹ (relative viscosity values ca. 1.185-1.449) was observed. The spectrophotometer detector sensitivity and the humidity of the samples did not influence the results. The methodology developed is interesting because it does not produce hazardous wastes, avoids the use of time-consuming chemical methods and can rapidly predict the intrinsic viscosity of PET samples over a large range of values, which includes those of recycled materials.     

Monitoring substrate and products in a bioprocess with FTIR spectroscopy coupled to artificial neural networks enhanced with a genetic-algorithm-based method for wavelength selection

An experiment was developed as a simple alternative to existing analytical methods for the simultaneous quantitation of glucose (substrate) and glucuronic acid (main product) in the bioprocesses Kombucha by using FTIR spectroscopy coupled to multivariate calibration (partial least-squares, PLS-1 and artificial neural networks, ANNs). Wavelength selection through a novel ranked regions genetic algorithm (RRGA) was used to enhance the predictive ability of the chemometric models. Acceptable results were obtained by using the ANNs models considering the complexity of the sample and the speediness and simplicity of the method. The accuracy on the glucuronic acid determination was calculated by analysing spiked real fermentation samples (recoveries ca. 115%).     

Assessment of infrared spectroscopy and multivariate techniques for monitoring the service condition of diesel-engine lubricating oils

This paper presents two methodologies for monitoring the service condition of diesel-engine lubricating oils on the basis of infrared spectra. In the first approach, oils samples are discriminated into three groups, each one associated to a given wear stage. An algorithm is proposed to select spectral variables with good discriminant power and small collinearity for the purpose of discriminant analysis classification. As a result, a classification accuracy of 93% was obtained both in the middle (MIR) and near-infrared (NIR) ranges. The second approach employs multivariate calibration methods to predict the viscosity of the lubricant. In this case, the use of absorbance measurements in the NIR spectral range was not successful, because of experimental difficulties associated to the presence of particulate matter. Such a problem was circumvented by the use of attenuated total reflectance (ATR) measurements in the MIR spectral range, in which an RMSEP of 3.8 cSt and a relative average error of 3.2% were attained.     

RELATIVE WIDTH OF SMOOTH CLASSES OF MULTIVARIATE PERIODIC FUNCTIONS WITH RESTRICTIONS ON ITERATED LAPLACE DERIVATIVES IN THE L2-METRIC

For two subsets W and V of a Banach space X, let Kn(W, V, X) denote the relative Kolmogorov n-width of W relative to V defined by Kn (W, V, X) := inf sup Ln f∈W g∈V∩Ln inf ‖f-g‖x,where the infimum is taken over all n-dimensional linear subspaces Ln of X. Let W2(△r) denote the class of 2w-periodic functions f with d-variables satisfying ∫[-π,π]d |△rf(x)|2dx ≤ 1,while △r is the r-iterate of Laplace operator △. This article discusses the relative Kolmogorov n-width of W2(△r) relative to W2(△r) in Lq([-r, πr]d) (1 ≤ q ≤∞), and obtain its weak asymptotic result.     

The Generalized Pairs Plot

This article develops a generalization of the scatterplot matrix based on the recognition that most datasets include both categorical and quantitative information. Traditional grids of scatterplots often obscure important features of the data when one or more variables are categorical but coded as numerical. The generalized pairs plot offers a range of displays of paired combinations of categorical and quantitative variables. A mosaic plot, fluctuation diagram, or faceted bar chart may be used to display two categorical variables. A side-by-side boxplot, stripplot, faceted histogram, or density plot helps visualize a categorical and a quantitative variable. A traditional scatterplot is suitable for displaying a pair of numerical variables, but options also support density contours or annotating summary statistics such as the correlation and number of missing values, for example. By combining these, the generalized pairs plot may help to reveal structure in multivariate data that otherwise might go unnoticed in the process of exploratory data analysis. Two different R packages provide implementations of the generalized pairs plot, gpairs and GGally. Supplementary materials for this article are available online on the journal web site.     

Stochastic Correlation and Volatility Mean-reversion – Empirical Motivation and Derivatives Pricing via Perturbation Theory

Abstract

The dependence structure is crucial when modelling several assets simultaneously. We show for a real-data example that the correlation structure between assets is not constant over time but rather changes stochastically, and we propose a multidimensional asset model which fits the patterns found in the empirical data. The model is applied to price multi-asset derivatives by means of perturbation theory. It turns out that the leading term of the approximation corresponds to the Black–Scholes derivative price with correction terms adjusting for stochastic volatility and stochastic correlation effects. The practicability of the presented method is illustrated by some numerical implementations. Furthermore, we propose a calibration methodology for the considered model.     

Development of a method based on sorbent trapping followed by solid-phase microextraction for the determination of synthetic musks in indoor air

Synthetic musks are extensively used as fragrance components in a wide range of consumer and personal care products such as detergents, shampoos, perfumes and other cosmetic products. Amongst them, galaxolide and tonalide have become ubiquitous pollutants due to their continuous releasing into the environment. Because of their nature as artificial fragrances, inhalation should be considered as an important exposure pathway, especially in indoor environments. However, up to now very few studies have been carried out to determine these emergent pollutants indoors. In this work, a simple and highly sensitive methodology for the analysis of synthetic musk fragrances in indoor air samples is presented. The proposed methodology combines solid-phase extraction (SPE) and solid-phase microextraction (SPME), followed by gas chromatography-mass spectrometry (GC/MS). To the best of our knowledge, this is the first method based on SPME for the analysis of musks in air. By active sampling, musks present in air were adsorbed onto 25mg Tenax and then transferred to a SPME fiber in the headspace mode (HS). An experimental design strategy was used to optimize main factors potentially affecting the microextraction process such as fiber coating, temperature and the addition of a microvolume of organic solvent to the solid sorbent prior to SPME. Breakthrough of the SPE sorbent was studied from 1 to 10m(3) without significant losses. Recovery studies were performed at two concentration levels (2 and 20ngm(-3)), obtaining quantitative recoveries (>/=85%) by external calibration. A comprehensive study was performed in order to estimate the limits of detection taking into account the contamination risks and laboratory blanks. Values at the sub ngm(-3) level were achieved for all the target compounds sampling 5m(3) air. External calibration, not requiring the complete sampling process, demonstrated to be suitable for the quantification of all musk compounds. Finally, several indoor environments were analyzed using the proposed method.     

Approach on Tsallis statistical interpretation of hydrogen-atom by adopting the generalized radial distribution function

This paper revisits the statistical interpretation of the hydrogen atom within the framework of Tsallis Statistical Mechanics in the Canonical Ensemble. The convergence of the partition function does not exhibit for all the temperatures, while the well-known T → T′ transformation method of Tsallis Statistics fails, since non-monotonicity is observed between the ordinary temperature, T, and the auxiliary one, T′. Here we re-examine the inconsistency of T → T′ transformation method, in the case where the partition function converges for all the temperatures, by considering the generalized radial distribution function. We find that both the transformation method inconsistency and the partition function divergence can be recovered for all the temperatures, if the hydrogen atom is restricted within a critical radius R _c  ≤ 4.832 bohr, while Tsallis entropic index values are given by . An erratum to this article can be found at