Optimal pricing for a heterogeneous portfolio for a given risk factor and convex distance measure

Consider a portfolio containing heterogeneous risks. The premiums of the policyholders might not cover the amount of the payments which an insurance company pays the policyholders. When setting the premium, this risk has to be taken into consideration. On the other hand the premium that the insured pays has to be fair. This fairness is measured by a function of the difference between the risk and the premium paid—we call this function a distance function. For a given small probability of insolvency, we find the premium for each class, such that the distance function is minimized. Next we formulate and solve the dual problem, which is minimizing the insolvency probability under the constraint that the distance function does not exceed a given level. This paper generalizes a previous paper [Zaks, Y., Frostig, E., Levikson, B., 2006. Optimal pricing of a heterogeneous portfolio for a given risk level. Astin Bull. 36 (1), 161–185] where only a square distance function was considered.     

Dispersion polymerization of styrene: Effect of surfactant

The influence of poly(vinyl alcohol) (PVA), a steric stabilizer, and sodium dodecyl sulfate (SDS), an electrostatic stabilizer, on the stability of styrene dispersion polymerized systems was studied. It was shown that in stabilization by PVA there was pronounced bridging of the submicron emulsion particles to 10-μ dispersion particles and that the emulsion particles could not be washed off. In SDS stabilization, on the other hand, the emulsion formed was easily washed off because bridging with SDS does not occur. The surface tension of the aqueous phase measured during polymerization showed different characteristics for stable and unstable systems.     

Decomposition of triacetone triperoxide is an entropic explosion

Both X-ray crystallography and electronic structure calculations using the cc-pVDZ basis set at the DFT B3LYP level were employed to study the explosive properties of triacetone triperoxide (TATP) and diacetone diperoxide (DADP). The thermal decomposition pathway of TATP was investigated by a series of calculations that identified transition states, intermediates, and the final products. Counterintuitively, these calculations predict that the explosion of TATP is not a thermochemically highly favored event. It rather involves entropy burst, which is the result of formation of one ozone and three acetone molecules from every molecule of TATP in the solid state.     

Superconductivity Near the Normal State Under the Action of Electric Currents and Induced Magnetic Fields in {\mathbb{R}^2}

We consider the linearization of the time-dependent Ginzburg-Landau system near the normal state. We assume that an electric current is applied through the sample, which captures the whole plane, inducing thereby, a magnetic field. We show that independently of the current, the normal state is always stable. Using Fourier analysis the detailed behaviour of solutions is obtained as well. Relying on semi-group theory we then obtain the spectral properties of the steady-state elliptic operator.     

Twist impeded self-diffusion in a cholesteric

Molecular self-diffusion along the pitch axis of a twisted nematic is measured by its motional averaging effect on the deuterium quadrupole interaction. The diffusion constant is found to decrease as the pitch length is decreased. This result is explained by simple phenomenological considerations and is consistent with published viscosity measurements.     

The effect of reverberation on the performance of cepstral mean subtraction in speaker verification

Speaker verification (SVR) performance is degraded under reverberation conditions. Cepstral mean subtraction (CMS) is often applied to the feature vectors in order to compensate for convolutive effects of transmission channels, which are considered to have a short-duration impulse response. The effect of reverberation on the performance of CMS applied to the feature vectors in SVR is investigated. Although CMS was found effective in reducing the effect of reverberation for short reverberation time (RT), in cases of long RT, it is shown that CMS may degrade SVR performance rather than improve it. Hence, CMS should not to be used in these cases. In addition, the effect of the room volume was tested and found less critical than the effect of long RT.     

A note on the variational formulation for quasi-linear initial-value problems

A variational formulation, equivalent to an initial-value problem for nonlinear systems, not necessarily self-adjoint, is derived with applications to linear and nonlinear wave problems and transonic aerodynamics.

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Résumé Nous présentons une formulation variationnelle pour les systèmes quasi-linéaires et leur applications aux ondes non-linéaires et l'écoulement transonique stationnaire.

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Work partially supported by Air-Force Grant No. AFOSR-73-2561.     

Variational multiple-tensor fitting of fiber-ambiguous diffusion-weighted magnetic resonance imaging voxels

Partial volume effects are often experienced in diffusion-weighted MRI of biologic tissue. This is when the signal attenuation reflects a mixture of diffusion processes, originating from different tissue compartments, residing in the same voxel. Decomposing the mixture requires elaborated models that account for multiple compartments, yet the fitting problem for those models is usually ill posed. We suggest a novel approach for stabilizing the fitting problem of the multiple-tensors model by a variational framework that adds biologically oriented assumption of neighborhood alignments. The framework is designed to address fiber ambiguity caused by a number of neuronal fiber compartments residing in the same voxel. The method requires diffusion data acquired by common, clinically feasible MRI sequences, and is able to derive familiar tensor quantities for each compartment. Neighborhood alignment is performed by adding piece-wise smooth regularization constraints to an energy function. Minimization with the gradient descent method produces a set of diffusion-reaction partial differential equations that describe a tensor-preserving flow towards a best approximation of the data while maintaining the constraints. We analyze fiber compartment separation capabilities on a synthetic model of crossing fibers and on brain areas known to have crossing fibers. We compare the results with diffusion tensor imaging analysis and discuss applications for the framework.     

Thin boundary layers of chiral smectics

We consider a reduced Landau–de Gennes energy functional which describes a chiral smectic liquid crystal with large elastic coefficients. We prove that, according to this model, chiral smectics exhibit behavior which is similar to surface superconductivity: a thin layer of smectics near the boundary, and cholesterics in the bulk of the material. We obtain this behavior for a wide region in the parameter space. We show that in a certain limit case this boundary layer can determine the direction of the helical axis of the cholesterics.