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.     

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.     

Outcomes matter: estimating pre-transplant survival rates of kidney-transplant patients using simulator-based propensity scores

The current kidney allocation system in the United States fails to match donors and recipients well. In an effort to improve the allocation system, the United Network of Organ Sharing (UNOS) defined factors that should determine a new allocation policy, and particularly patients’ potential remaining lifetime without a transplant (pre-transplant survival rates). Estimating pre-transplant survival rates is challenging because the data available on candidates and organ recipients is already “contaminated” by the current allocation policy. In particular, the selection of patients who are offered (and decide to accept) a kidney is not random. We therefore expect differences in mortality-related characteristics of organ recipients and of candidates who have not received transplant. Such differences introduce bias into survival models. Existing approaches for tackling this selection bias either ignore the difference between candidates and recipients or assume that selection to transplant is based solely on patients’ pre-transplant information, irrespective of the potential allocation outcome. We argue that in practice the allocation is dependent on the anticipated allocation outcome, which is a major factor in selection to transplant. Moreover, we show that ignoring the anticipated outcome increases model bias rather than decreases it. In this paper, we propose a novel simulator-based approach (SimBa) that adjusts for the selection bias by taking into account both pre-transplant and anticipated outcome information using simulation. We then fit survival models to kidney transplant waitlist data and compare the different adjustment methods. We find that SimBa not only fits the data best, but also captures a key aspect of the current allocation policy, namely, that the probability of kidney allocation increases in the expected pre-transplant life years.     

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.     

Latrunculin,a new 2-thiazolidinone macrolide from the marine sponge latrunculia magnifica

Three new toxins were isolated from the Red Sea sponge $\text{Latrunculia magnifica}$ A full structure determination of these toxins, by spectroscopic methods, was aided by an X-ray diffraction analysis of a crystalline derivative ($\text{1}$b) of latrunculin-A. The Latrunculins exhibit a new class of 14 and 16 membered macrolides to which the rare 2-thiazolidinone moiety is attached. A biogenesis of these biologically active compounds is put forward.     

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.     

Acyclic Hypergraph Projections

Hypergraphs can be partitioned into two classes: tree (acyclic) hypergraphs and cyclic hypergraphs. This paper analyzes a new class of cyclic hypergraphs called Xrings. HypergraphHis an Xring if the hyperedges ofHcan be circularly ordered so that for every vertex, all hyperedges containing the vertex are consecutive; in addition, the vertices of no hyperedge may be a subset of the vertices of another hyperedge, and no vertex may appear in exactly one hyperedge. LetH₁andH₂be two hypergraphs. A tree projection ofH₁with respect toH₂is an acyclic hypergraphH₃such that the vertices of each hyperedge inH₁appear among the vertices of some hyperedge ofH₃and the vertices of each hyperedge inH₃appear among the vertices of some hyperedge ofH₂. A polynomial time algorithm is presented for deciding, given XringH₁and arbitrary hypergraphH₂, whether there exists a tree projection ofH₂with respect toH₁. It is shown that hypergraphHis an Xring iff a modified adjacency graph ofHis a circular-arc graph. A linear time Xring recognition algorithm, for GYO reduced hypergraphs as inputs, is presented.     

On generating multivariate Poisson data in management science applications

Generating multivariate Poisson random variables is essential in many applications, such as multi echelon supply chain systems, multi‐item/multi‐period pricing models, accident monitoring systems, etc. Current simulation methods suffer from limitations ranging from computational complexity to restrictions on the structure of the correlation matrix, and therefore are rarely used in management science. Instead, multivariate Poisson data are commonly approximated by either univariate Poisson or multivariate Normal data. However, these approximations are often not adequate in practice. In this paper, we propose a conceptually appealing correction for NORTA (NORmal To Anything) for generating multivariate Poisson data with a flexible correlation structure and rates. NORTA is based on simulating data from a multivariate Normal distribution and converting it into an arbitrary continuous distribution with a specific correlation matrix. We show that our method is both highly accurate and computationally efficient. We also show the managerial advantages of generating multivariate Poisson data over univariate Poisson or multivariate Normal data. Copyright © 2011 John Wiley & Sons, Ltd.