VaR and ES for linear portfolios with mixture of elliptic distributions risk factors

In this paper, we generalize the Linear VaR method from portfolios with normally distributed risk factors to portfolios with mixture of elliptically distributed ones. We treat both the Expected Shortfall and the Value-at-Risk of such portfolios. Special attention is given to the particular case of a mixture of multivariate t-distributions. This is a part of J. SADEFO-KAMDEM PhD Thesis[12] of the Université de Reims, France . It has been presented at the workshop on modelling and computation in Financial Engineering at Bad Herrenalb, Germany May 6-8, 2003. The author is an associate professor at the Department of mathematics, université d’Evry Val d’Essonne.     

On the recent papers by Nagode et al.

The recent work Professor Nagode and colleagues is discussed with respect to the use of mixture Weibull models.     

Inference for pth‐order random coefficient integer‐valued autoregressive processes

Abstract. A pth‐order random coefficient integer‐valued autoregressive [RCINAR(p)] model is proposed for count data. Stationarity and ergodicity properties are established. Maximum likelihood, conditional least squares, modified quasi‐likelihood and generalized method of moments are used to estimate the model parameters. Asymptotic properties of the estimators are derived. Simulation results on the comparison of the estimators are reported. The models are applied to two real data sets.     

Almost k-wise independence versus k-wise independence

We say that a distribution over {0,1}ⁿ is (ε,k)-wise independent if its restriction to every k coordinates results in a distribution that is ε-close to the uniform distribution. A natural question regarding (ε,k)-wise independent distributions is how close they are to some k-wise independent distribution. We show that there exist (ε,k)-wise independent distributions whose statistical distance is at least n^O(k)·ε from any k-wise independent distribution. In addition, we show that for any (ε,k)-wise independent distribution there exists some k-wise independent distribution, whose statistical distance is n^O(k)·ε.     

Synthesis and characterization of acidic properties of Al-SBA-15 materials with varying Si/Al ratios

Al-SBA-15 of varying Si/Al ratios in the range 11.4–78.4 was synthesized using tri-block copolymer P123. The calcined materials were examined by XRD, pore size distribution, surface area, ²⁷Al NMR spectroscopy. The acidity and acid strength distribution were studied using microcalorimetric adsorption of NH₃. The acidic properties were also examined by cumene cracking reaction as a function of Si/Al ratios. Systematic variation of acidity and activity was observed as a function of Si/Al ratio. The initial heats of NH₃ adsorption correlated well with activity indicate that acid sites with ΔH > 100 kJ/mole is responsible for cumene cracking activity. Linear correlations were obtained with total acidity and cumene cracking activities. The tetrahedral aluminum was found to be responsible for the observed acidities and catalytic activities.     

Parametric and nonparametric Bayesian model specification: A case study involving models for count data

In this paper we present the results of a simulation study to explore the ability of Bayesian parametric and nonparametric models to provide an adequate fit to count data of the type that would routinely be analyzed parametrically either through fixed-effects or random-effects Poisson models. The context of the study is a randomized controlled trial with two groups (treatment and control). Our nonparametric approach uses several modeling formulations based on Dirichlet process priors. We find that the nonparametric models are able to flexibly adapt to the data, to offer rich posterior inference, and to provide, in a variety of settings, more accurate predictive inference than parametric models.     

The Bivariate Transmuted Family of Distributions: Theory and Applications

The bivariate distributions are useful in simultaneous modeling of two random variables. These distributions provide a way to model models. The bivariate families of distributions are not much widely explored and in this article a new family of bivariate distributions is proposed. The new family will extend the univariate transmuted family of distributions and will be helpful in modeling complex joint phenomenon. Statistical properties of the new family of distributions are explored which include marginal and conditional distributions, conditional moments, product and ratio moments, bivariate reliability and bivariate hazard rate functions. The maximum likelihood estimation (MLE) for parameters of the family is also carried out. The proposed bivariate family of distributions is studied for the Weibull baseline distributions giving rise to bivariate transmuted Weibull (BTW) distribution. The new bivariate transmuted Weibull distribution is explored in detail. Statistical properties of the new BTW distribution are studied which include the marginal and conditional distributions, product, ratio and conditional momenst. The hazard rate function of the BTW distribution is obtained. Parameter estimation of the BTW distribution is also done. Finally, real data application of the BTW distribution is given. It is observed that the proposed BTW distribution is a suitable fit for the data used.     

Equations of state for hard-sphere fluids

Equations of state and contact values of hard-sphere radial distribution functions (rdf's) which are given by a linear combination of the Percus— Yevick and scaled-particle virial expressions are considered. In the one-component case the mixing coefficient() is, in general, a function of the volume fraction. In mixtures the coefficient( _i ,d _i ), in general, depends upon the volume fraction _i , and diameterd _i , of each species,i andj. For the contact valuesY _ij of the rdf's, the mixing coefficients _ij ( _k ) also depend on speciesi andj. Density expansions for the exact for the one-component hard-sphere fluid are obtained and compared with several approximations made in earlier works and in our own work, as well as with simulations. For a mixture, it turns out that one cannot obtain the exact fourth virial coefficient by using a linear combination of the Percus-Yevick and scaled-particle virial expressions forY _ij unless one allows _ij to depend on mole fractionsx _i even at the zeroth order of its density expansion. We also find that _ij must depend on particle speciesi andj in order to satisfy the exact limits obtained earlier by Sung and Stell. A new equation of state for the binary hard-sphere mixture which satisfies all the exact limits we have considered is suggested.Paper presented at the Tenth Symposium on Thermophysical Properties, June 20–23, 1988, Gaithersburg, Maryland, U.S.A.     

Within-plant variation in concentrations of amino acids,sugar, and sinigrin in phloem sap of black mustard,Brassica nigra (L.) Koch (Cruciferae)

Although within-plant variation in the nutrient and allelochemical composition of phloem sap has been invoked to explain patterns of host use by phloem-feeding insects, little is known about within-plant variation in phloem chemistry. Here I describe a new technique in which I use the green peach aphid,Myzus persicae Sulz., to investigate within-plant variation in the concentrations of chemicals in the phloem sap of black mustard,Brassica nigra (L.) Koch (Cruciferae). Relationships between the concentrations of chemicals in aphid diets and honeydew were established using honeydew from aphids fed on artificial diets with known concentrations of amino acids, sucrose, and sinigrin. These relationships were applied to honeydew from aphids fed on different aged leaves of black mustard to estimate the concentrations of the chemicals in phloem sap. Sinigrin concentration was estimated to be high (>10 mM) in phloem sap in young leaves, calling into question the prevailing opinion that phloem sap contains only low concentrations of allelochemicals. High concentrations may function as defenses against sap-feeding herbivores. Within-plant variation in phloem sap composition was high: (1) young leaves had high concentrations of nutrients (216 mM amino acids, 26% sugar) and sinigrin (>10 mM); (2) mature and presenescent leaves had lower concentrations of nutrients (77–83 mM amino acids, 19–20% sugar) and low concentrations of sinigrin (1–2 mM); and (3) senescing leaves had high concentrations of nutrients (199 mM amino acids, 25% sugar) and low concentrations of sinigrin (3 mM).