Optimal reinsurance under risk and uncertainty

This paper deals with the optimal reinsurance problem if both insurer and reinsurer are facing risk and uncertainty, though the classical uncertainty free case is also included. The insurer and reinsurer degrees of uncertainty do not have to be identical. The decision variable is not the retained (or ceded) risk, but its sensitivity with respect to the total claims. Thus, if one imposes strictly positive lower bounds for this variable, the reinsurer moral hazard is totally eliminated.Three main contributions seem to be reached. Firstly, necessary and sufficient optimality conditions are given in a very general setting. Secondly, the optimal contract is often a bang–bang solution, i.e., the sensitivity between the retained risk and the total claims saturates the imposed constraints. Thirdly, the optimal reinsurance problem is equivalent to other linear programming problem, despite the fact that risk, uncertainty, and many premium principles are not linear. This may be important because linear problems may be easily solved in practice, since there are very efficient algorithms.     

Application of transparent boundary conditions to high-order finite-difference schemes for the wave equation in waveguides

We propose a method for generating finite-difference approximations of transparent boundary conditions (TBCs) with the fourth and sixth order in space. It is based on the wave equation solution continuation extra two or three layers of grid points outside the computational domain to use them in central-difference operators on approaching the boundary. We present the theoretical background of the method, give estimates of computational resources, and discuss accuracy and stability results of numerical tests in 1D and 2D cases.     

A stochastic control model of investment,production, and consumption on a finite horizon

In this paper, we consider a stochastic control problem on a finite time horizon. The unit price of capital obeys a logarithmic Brownian motion, and the income from production is also subject to the random Brownian fluctuations. The goal is to choose optimal investment and consumption policies to maximize the finite horizon expected discounted hyperbolic absolute risk aversion utility of consumption. A dynamic programming principle is used to derive a time‐dependent Hamilton–Jacobi–Bellman equation. The Leray–Schauder fixed point theorem is used to obtain existence of solution of the HJB equation. At last, we derive the optimal investment and consumption policies by the verification theorem. The main contribution in this paper is the use of PDE technique to the finite time problem for obtaining optimal polices. Copyright © 2014 John Wiley & Sons, Ltd.     

Optimal and approximate boundary controls of an elastic body with quasistatic evolution of damage

In this paper, we study an optimal control problem for the mixed boundary value problem for an elastic body with quasistatic evolution of an internal damage variable. We suppose that the evolution of microscopic cracks and cavities responsible for the damage is described by a nonlinear parabolic equation. A density of surface traction p acting on a part of boundary of an elastic body Ω is taken as a boundary control. Because the initial boundary value problem of this type can exhibit the Lavrentieff phenomenon and non‐uniqueness of weak solutions, we deal with the solvability of this problem in the class of weak variational solutions. Using the convergence concept in variable spaces and following the direct method in calculus of variations, we prove the existence of optimal and approximate solutions to the optimal control problem under rather general assumptions on the quasistatic evolution of damage. Copyright © 2014 John Wiley & Sons, Ltd.     

Approximation properties for solutions to non‐Lipschitz stochastic differential equations with Lévy noise

In this paper, we consider the non‐Lipschitz stochastic differential equations and stochastic functional differential equations with delays driven by Lévy noise, and the approximation theorems for the solutions to these two kinds of equations will be proposed respectively. Non‐Lipschitz condition is much weaker condition than the Lipschitz one. The simplified equations will be defined to make its solutions converge to that of the corresponding original equations both in the sense of mean square and probability, which constitute the approximation theorems. Copyright © 2014 John Wiley & Sons, Ltd.     

Addendum to “Switching effect and the metal–insulator transition in electric field” by A.L. Pergament et al. [J. Phys. Chem. Solids 71 (2010) 874]

In the paper mentioned above we reported on the switching mechanism in vanadium dioxide which was shown to be based on the electronically-induced Mott insulator-to-metal transition occurring in conditions of the non-equilibrium carrier density excess in the applied electric field, and the proposed model involved the dependence of the carrier density n on electric field (the Poole–Frenkel effect), as well as the dependence of the critical electric field on n. The data on the n(T) dependence were obtained on the assumption of a temperature-independent carrier mobility μ, and the problem of n reduction at lower temperatures was not fully understood. In this Letter we revisit this problem in the light of some recent data on the μ(T) dependence for VO₂. It is shown that the adjusted values of n, taking into account this μ(T), correspond to the Mott critical density within an order of magnitude.     

Enhanced depolarization temperature in 0.90NBT–0.05KBT–0.05BT ceramics induced by BT nanowires

The depolarization temperature (T_d) of piezoelectric materials is an important figure of merit for their application at elevated temperatures. This study focuses on the effect of BaTiO₃ (BT) nanowires on T_d and piezoelectric properties of morphotropic-phase-boundary 0.90NBT–0.05KBT–0.05BT ceramics. The results reveal that BaTiO₃ nanowires can pin the domain wall, leading to the increase of coercive field (E_c) from 21.06 kV/cm to 34.99 kV/cm. The T_d value of 0.90NBT–0.05KBT–0.05BT ceramics can be enhanced approximately 20 °C when using BT nanowires instead of BT solution as the raw material. Meanwhile, at the same polarization conditions, the piezoelectric constant of the ceramic added BT nanowires (172 pC/N) is decreased but still remains a larger value compared with those of other lead-free ceramics. The results imply that the addition of BT nanowires into NBT–KBT is a very effective route to improve T_d.     

EPR,ENDOR and optical spectroscopy of Yb3+ ion in KZnF3 single crystals

The paramagnetic center of tetragonal symmetry formed by the Yb³⁺ ion in the KZnF₃ crystal has been studied using methods of EPR, ENDOR and optical spectroscopy. The location of the impurity ion and the structural model of the complex differing from the model of the Yb³⁺ center in KMgF₃ have been established. The empirical scheme of the energy levels of the Yb³⁺ ion has been found. The parameters of its interaction with the crystal electrostatic field and the hyperfine interaction with ligands of the nearest environment have been determined. The parameters of the crystal field were used for the analysis of the distortions of the crystal lattice in the vicinity of Yb³⁺. The parameters of the transferred hyperfine interaction have been calculated for the distances between Yb³⁺ and F⁻ ions of the nearest environment obtained taking into account the found distortions. They are in good agreement with the experimental values.     

BaCO3 mediated modifications in structural and magnetic properties of natural nanoferrites

Preparing M-type barium hexaferrite and improving the magnetic response of natural ferrites by incorporating barium carbonate (BaCO₃) is ever-demanding. Series of barium carbonate doped ferrites with composition (100−x)Fe₃O₄·xBaCO₃ (x=0, 10, 20, 30 wt%) are prepared through solid state reaction method and sintered gradually at temperatures of 800 and 1000 °C. Nanoparticles of natural ferrite and commercial BaCO₃ are used as raw materials. Impacts of BaCO3 on structural and magnetic properties of these synthesized ferrites are inspected. The obtained ferrites are characterized using scanning electron microscopy (SEM), X-ray diffraction (XRD) and vibrating sample magnetometer (VSM) at room temperature. Uniform barium hexaferrite particles in terms of both morphology and size are not achieved. The average crystallite size of BaFe₁₂O₁₉ is observed to be within 30–600 nm. The sintering process results phase transformation from Fe₃O₄ (magnetite) to α-Fe₂O₃ (hematite) and the formation of hexagonal barium ferrite crystals. The occurrence of barium crystal is found to enhance with the increase of BaCO₃ concentrations up to 20 wt% and suddenly drop at 30 wt%. Saturation and remanent magnetization of the doped ferrites are significantly augmented up to 16.37 and 8.92 emu g⁻¹, respectively compared to their pure counterpart. Furthermore, the coercivity field is slightly decreased as BaCO₃ concentrations are increased. BaCO₃ mediated improvements in the magnetic response of natural ferrites are demonstrated.