Correlation of defaults in complex portfolios using copula techniques

This work, dealing with the correlation between subportfolios in more complex portfolios, begins with a brief survey of the necessary theoretical background. The basic statistical and probabilistic concepts are reviewed. The notion of copulas is introduced along with the fundamental theorem of Sklar. After this background a numerical procedure and code are developed for correlated defaults in multiple correlated portfolio. Further on, interesting results regarding the impact of changes in correlation on the portfolio performance are investigated in the simulations. The most valuable observations regarding the expected default ratios of two subportfolios considered jointly are presented and explained with particular care. These observations are compared with theoretical results. The sensitivity of the tranche losses to correlation parameters is examined carefully. The work is concluded with a brief summary of the most significant observations and their possible impact on portfolio performance

Friction and Wear at Elevated Velocities

Severe contact stress problems generate high temperature and create thermomechanical gouging and wear due to high velocity sliding between contacting materials. The major consideration is to develop an experimental and theoretical model for the material constitutive behavior in order to better characterize and predict the internal failure surroundings the gouging and wear events and understand the physical behavior of high speed contact environment. An enhancement of an existing tribometer device developed by Philippon et al. [2004] is made up of a dynamometer ring and a load sensor that allows to apply an apparent normal force on specimens and measure frictional forces, respectively. The setup has been adapted on a hydraulic testing machine and pressure gas gun to carry out Steel 1080 on Steel VascoMax experiments. The recordings of the normal and tangential forces allows the determination of the friction coefficient. The effects of the sliding velocity on the surface roughness and the dry fiction coefficient are investigated. Performed scans (SEM) show the roughness decrease and reveal the occurrence of the wear. The second part is devoted to the theoretical approach capturing the phenomena of the wear with extension to incorporate gauging problems. The principle of virtual power is used by introducing the contributions from damage and its corresponding gradients. In addition two internal state variables are introduced on the frictional contact interface measuring the tangential slip and the wear. The constitutive model is formulated with state laws based on the free energies and the complimentary laws based on the dissipation potentials. The proposed model is implemented as user defined subroutine VUMAT in ABAQUS Explicite to analyze the structural response of the high speed sliding experiment from the first part. This model provides a potential feature to relate the non-local continuum plasticity and damage of the bulk material to friction and wear at the contact interfaces. This research is invaluable in providing a multiscale material model and numerical procedure that will be used within a hydrocode to better facilitate the design components of the severe contact stress applications