Convex combinations of quadrant dependent copulas

It is well known that quadrant dependent (QD) random variables are also quadrant dependent in expectation (QDE). Recent literature has offered examples rigorously establishing the fact that there are QDE random variables which are not QD. The examples are based on convex combinations of specially chosen QD copulas: one negatively QD and another positively QD. In this paper we establish general results that determine when convex combinations of arbitrary QD copulas give rise to negatively or positively QD/QDE copulas. In addition to being an interesting mathematical exercise, the established results are helpful when modeling insurance and financial portfolios.     

Background Risk Models and Stepwise Portfolio Construction

Assuming the multiplicative background risk model, which has been a popular model due to its practical applicability and technical tractability, we develop a general framework for analyzing portfolio performance based on its subportfolios. Since the performance of subportfolios is easier to assess, the herein developed stepwise portfolio construction (SPC) provides a powerful alternative to a number of traditional portfolio construction methods. Within this framework, we discuss a number of multivariate risk models that appear in the actuarial and financial literature. We provide numerical and graphical examples that illustrate the SPC technique and facilitate our understanding of the herein developed general results.     

Risk measures, distortion parameters, and their empirical estimation

Risk measures are of considerable current interest. Among other uses, they allow an insurer to calculate a risk-loaded premium for a random loss. However, the premium principle in use by the insurer may be, at least in part, based on considerations other than risk. It is then important to quantify the degree to which the premium compensates the insurer for the risk associated with the loss. This can be done by choosing a suitable risk measure and solving for the parameter that leads to the insurer’s premium. When the loss distribution is unknown, this becomes a statistical estimation problem.In this paper, we investigate the nonparametric estimation of the parameter associated with a distortion-based risk measure. It is assumed that the premium principle is known, but no information is assumed about the loss distribution, and therefore empirical estimators are used. We explore the asymptotic properties of the resulting estimator of the risk measure parameter in general and for three well-known risk measures in particular: the proportional hazards transform, the Wang transform, and the conditional tail expectation.     

Synthesis and characterization of layered double hydroxides with different cations (Mg,Co, Ni,Al), decomposition and reformation of mixed metal oxides to layered structures

Three layered double hydroxides (LDH) [Mg_1−xAl_x(OH)₂]^x+(A^m−)_x/m]·nH₂O and [M^II _1−xM^III _x (OH)₂]^x+(A^m−)_x/m]·nH₂O (M^II — Mg, Co, Ni; MIII — Al; A — CO₃ ²⁻) were successfully synthesized by the low supersaturation method. The as-synthesized LDH samples were thermally decomposed and the derived mixed metal oxides reformed back to layered structures in water and magnesium nitrate media at different temperatures. All synthesized samples were characterized by X-ray diffraction (XRD) analysis, thermogravimetric (TG) analysis, X-ray fluorescence (XRF) analysis and scanning electron microscopy (SEM). The results of XRD and XRF analyses showed that single-phase layered double hydroxides were formed during synthesis and reformation. It was demonstrated, that a partially substituted by cobalt and nickel LDH samples also show memory effect. The crystallite size of regenerated LDH depends on the regeneration media, temperature and chemical composition. The LDH samples after regeneration consist of large particles with sharp edges along with a large amount of smaller particles     

Estimating the Index of Increase via Balancing Deterministic and Random Data

We introduce and explore an empirical index of increase that works in both deterministic and random environments, thus allowing to assess monotonicity of functions that are prone to random measurement errors. We prove consistency of the index and show how its rate of convergence is influenced by deterministic and random parts of the data. In particular, the obtained results suggest a frequency at which observations should be taken in order to reach any pre-specified level of estimation precision.We illustrate the index using data arising from purely deterministic and error-contaminated functions, which may or may not be monotonic.     

Strong laws for generalized absolute Lorenz curves when data are stationary and ergodic sequences

We consider generalized absolute Lorenz curves that include, as special cases, classical and generalized -statistics as well as absolute or, in other words, generalized Lorenz curves. The curves are based on strictly stationary and ergodic sequences of random variables. Most of the previous results were obtained under the additional assumption that the sequences are weakly Bernoullian or, in other words, absolutely regular. We also argue that the latter assumption can be undesirable from the applications point of view.

     

Interactions between bottle-brush polyelectrolyte layers: effects of ionic strength and oppositely charged surfactant

Interactions between cationic bottle-brush polyelectrolyte layers adsorbed on mica across salt and oppositely charged surfactant solutions were investigated with the interferometric surface force apparatus, and the results were compared with what is known for similarly charged linear polyelectrolytes. Ellipsometric measurements demonstrated that the bottle-brush polyelectrolytes, which contain 45 units long poly(ethylene oxide) side chains, are more readily desorbed than linear equivalents when the ionic strength of the solution is increased. It is argued that this is due to the steric repulsion between the poly(ethylene oxide) side chains that reduces the surface affinity. The preadsorbed bottle-brush polyelectrolyte layers were also exposed to sodium dodecyl sulfate (SDS) solutions. It was found that the presence of SDS affected the force profiles less than observed for similarly charged linear polyelectrolytes. This observation was attributed to excluded volume constraints imposed by the poly(ethylene oxide) side chains that reduces the accessibility of the charged polyelectrolyte segments and counteracts formation of large aggregates within the layer.     

Desorption of bottle-brush polyelectrolytes from silica by addition of linear polyelectrolytes studied by QCM-D and reflectometry

The possibility of exchanging adsorbed layers of PEO(45)MEMA:METAC-X brush polyelectrolytes (with two different charge densities, 10 and 75 mol%, denoted by X), with poly(MAPTAC), a highly charged linear polyelectrolyte, was investigated by quartz crystal microbalance with dissipation and reflectometry. The studies were conducted on a silica substrate at pH 10, conditions under which only electrostatic interactions are effective in the adsorption process. Based on the results, it was concluded that PEO(45)MEMA:METAC-10 forms an inhomogeneous layer at the interface through which poly(MAPTAC) chains can easily diffuse to reach the surface. On the other hand, the PEO(45)MEMA:METAC-75 layer was not affected when exposed to a poly(MAPTAC) solution. We argue that the observed effect for PEO(45)MEMA:METAC-75 is due to the formation of a homogeneous protective brush layer, in combination with the small difference in surface affinity between the bottle-brush polyelectrolyte and poly(MAPTAC), together with the difficulty of displacing highly charged polyelectrolyte chains once they are adsorbed on the oppositely charged surface. We also use the combination of QCM-D and reflectometry data to calculate the water content and layer thickness of the adsorbed layers.     

Adsorption characteristics of bottle-brush polymers on silica: effect of side chain and charge density

The adsorption behavior of bottle-brush polymers with different charge/PEO ratio on silica was studied using optical reflectometry and QCM-D. The results obtained under different solution conditions clearly demonstrate the existence of two distinct adsorption mechanisms depending on the ratio of charge/PEO. In the case of low-charge density brush polymers (0-10 mol %), the adsorption occurs predominantly through the PEO side chains. However, the presence of a small amount of charge along the backbone (as low as 2 mol %) increases the adsorption significantly above that of the uncharged bottle-brush polymer in pure water. As the charge density of the brush polymers is increased to 25 mol % or larger the adsorption occurs predominantly through electrostatic interactions. The adsorbed layer structure was studied by measuring the layer dissipation using QCM-D. The adsorbed layer formed by the uncharged brush polymer dissipates only a small amount of energy that indicates that the brush lie along the surface, the scenario in which the maximum number of PEO side chains interact with the surface. The adsorbed layers formed by the low-charge density brush polymers (2-10 mol %) in water are more extended, which results in large energy dissipation, whereas those formed by the high-charge density brush polymers (50-100 mol %) have their backbone relatively flat on the surface and the energy dissipation is again low.