Optimal Exercise Strategies for Operational Risk Insurance via Multiple Stopping Times

In this paper we demonstrate how to develop analytic closed form solutions to optimal multiple stopping time problems arising in the setting in which the value function acts on a compound process that is modified by the actions taken at the stopping times. This class of problem is particularly relevant in insurance and risk management settings and we demonstrate this on an important application domain based on insurance strategies in Operational Risk management for financial institutions. In this area of risk management the most prevalent class of loss process models is the Loss Distribution Approach (LDA) framework which involves modelling annual losses via a compound process. Given an LDA model framework, we consider Operational Risk insurance products that mitigate the risk for such loss processes and may reduce capital requirements. In particular, we consider insurance products that grant the policy holder the right to insure k of its annual Operational losses in a horizon of T years. We consider two insurance product structures and two general model settings, the first are families of relevant LDA loss models that we can obtain closed form optimal stopping rules for under each generic insurance mitigation structure and then secondly classes of LDA models for which we can develop closed form approximations of the optimal stopping rules. In particular, for losses following a compound Poisson process with jump size given by an Inverse-Gaussian distribution and two generic types of insurance mitigation, we are able to derive analytic expressions for the loss process modified by the insurance application, as well as closed form solutions for the optimal multiple stopping rules in discrete time (annually). When the combination of insurance mitigation and jump size distribution does not lead to tractable stopping rules we develop a principled class of closed form approximations to the optimal decision rule. These approximations are developed based on a class of orthogonal Askey polynomial series basis expansion representations of the annual loss compound process distribution and functions of this annual loss.     

Linear relationship between the first invariants of the stress and strain tensors in theories of plasticity with strain hardening

Energy-coupled stress and strain measures are defined in Euler coordinates. They are used to analyze the relationship between the first invariants of the stress and strain tensors for linearity and to determine strains at which the plastic component of the first strain invariant can be neglected. It is established that this relationship remains linear within an engineering plastic-strain tolerance of 0.2% irrespective of the value of strain intensity, which depends on the type of material and its stress state __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 3, pp. 60–72, March 2007.     

On Scalar Functionals of Nonlinear tensorial Constitutive Equations in the Theory of Plasticity for Nonisothermal Rectilinear Processes of Deformation

Based on base experiments formulated, methods are proposed to specify the scalar functional in the nonlinear equations that relate generalized stresses and finite strains in the theory of plasticity. The base experiments are conducted and the functionals are specified. It is shown that the nonlinear tensorial constitutive equations can be used to describe a nonisothermal process of deformation along a rectilinear path, which is distinct from the base ones, at high temperatures that cause creep strains     

Thermodynamic properties of liquid alloys Ni-Eu and Ni-Yb

Mixing enthalpies of melts of the binary Ni-Eu (0 < x _Ni < 0.89) and Ni-Yb (0 < x _Ni < 1) systems at 1300–1750 K were investigated using the isoperibolic calorimetry. They have alternating signs depending on the melt concentration. With the combined analysis of the data determined by us and in literature, the models of the liquid and solid alloys were obtained, and the phase diagrams were calculated.     

Approximation of solutions of stochastic differential equations with fractional Brownian motion by solutions of random ordinary differential equations

We prove a general theorem on the convergence of solutions of stochastic differential equations. As a corollary, we obtain a result concerning the convergence of solutions of stochastic differential equations with absolutely continuous processes to a solution of an equation with Brownian motion.     

Degeneration of plane affine Stolyarov connections

Consider a distribution of a plane in a projective space. A way of defining a plane affine Stolyarov connection associated with this distribution is proposed. It is set by the field of a connection object consisting of a connection quasitensor and a linear connection object. The object of this generalized affine connection defines torsion and curvature objects. We show that these objects are tensors. Conditions under which a plane affine Stolyarov connection is torsion-free or curvature-free are described. It is proved that the generalized affine connection with the connection quasitensor is the generalized Kronecker symbol degenerated into a linear connection.     

Effect of High-Temperature Electrochemical Deposition of Mo<Subscript>2</Subscript>C Coatings on the Corrosion and Electrochemical Behavior of Titanium

The possibility of increasing the corrosion resistance of titanium by electroplating molybdenum carbide coatings from the melts was studied.     

5-Diazouracils in Azo Coupling Reactions

6-Hydroxy-5-diazo-6H-uracil and 6-hydroxy-5-diazo-1,3-dimethyl-6H-uracil enter into azo coupling reaction with CH-acids, active phenols, arylamines, and heterocycles. The conditions of reaction depend on the substrate character.     

Polarization modulation of light in an optical waveguide under lateral compression

It is shown that a lateral pressure applied to a circular single-mode optical waveguide changes the phase difference between two orthogonally polarized modes and thereby modulates the polarization state of light (elastooptic effect). The efficiency of polarization modulation is characterized by a strain-to-phase difference conversion factor as applied to polarization modes of the fiber. An expression relating the phase difference between the modes and the displacement of squeezing plates is obtained and checked in real experiments and numerically. The efficiency of conversion of lateral pressure to phase difference between the polarization modes is shown to be fairly high, on the order of 10⁴ rad/(μm m).