Credit Risk Meets Random Matrices: Coping with Non-Stationary Asset Correlations

We review recent progress in modeling credit risk for correlated assets. We start from the Merton model which default events and losses are derived from the asset values at maturity. To estimate the time development of the asset values, the stock prices are used whose correlations have a strong impact on the loss distribution, particularly on its tails. These correlations are non-stationary which also influences the tails. We account for the asset fluctuations by averaging over an ensemble of random matrices that models the truly existing set of measured correlation matrices. As a most welcome side effect, this approach drastically reduces the parameter dependence of the loss distribution, allowing us to obtain very explicit results which show quantitatively that the heavy tails prevail over diversification benefits even for small correlations. We calibrate our random matrix model with market data and show how it is capable of grasping different market situations. Furthermore, we present numerical simulations for concurrent portfolio risks, i.e., for the joint probability densities of losses for two portfolios. For the convenience of the reader, we give an introduction to the Wishart random matrix model.Comment: Review of a new random matrix approach to credit ris

Early prediction of pulmonary outcomes in preterm infants using electrical impedance tomography

INTRODUCTION Electrical impedance tomography (EIT) allows assessment of ventilation and aeration homogeneity which may be associated with respiratory outcomes in preterm infants. METHODS This was a secondary analysis to a recent randomized controlled trial in very preterm infants in the delivery room (DR). The predictive value of various EIT parameters assessed 30 min after birth on important respiratory outcomes (early intubation <24 h after birth, oxygen dependency at 28 days after birth, and moderate/severe bronchopulmonary dysplasia; BPD) was assessed. RESULTS Thirty-two infants were analyzed. A lower percentage of aerated lung volume [OR (95% CI) = 0.8 (0.66-0.98), p = 0.027] as well as a higher aeration homogeneity ratio (i.e., more aeration in the non-gravity-dependent lung) predicted the need for supplemental oxygen at 28 days after birth [9.58 (5.16-17.78), p = 0.0028]. Both variables together had a similar predictive value to a model using known clinical contributors. There was no association with intubation or BPD, where numbers were small. DISCUSSION In very preterm infants, EIT markers of aeration at 30 min after birth accurately predicted the need for supplemental oxygen at 28 days after birth but not BPD. EIT-guided individualized optimization of respiratory support in the DR may be possible

Status Quo der Integrierten Versorgung in Deutschland: eine empirische Analyse

"Im internationalen Vergleich wird das deutsche Gesundheitssystem als ein System mit hoher Qualität in der Versorgungsleistung eingestuft. Dennoch findet innerhalb des Gesundheitssystems keine optimale Allokation der zur Verfügung stehenden Ressourcen statt. Reformbemühungen im Hinblick auf Einsparungs- und Wirtschaftlichkeitspotentia-len stehen an der Tagesordnung – so der jüngste Versuch der Bundesregierung im Juli 2006 mithilfe des veröffentlichten Eckpunktepapiers tiefsitzende Probleme an der Wurzel zu packen. Unerfüllte Erwartungen an die Eckpunkte zur Gesundheitsre-form geben jedoch keinen Anlass, das deutsche Gesundheitswesen nicht als ein Sys-tem zu begreifen, welches zahlreiche Gestaltungsmöglichkeiten in sich trägt. Eine zentrale Rolle spielen dabei Maßnahmen zur Stärkung der Integrierten Versorgung. Durch die Vernetzung der Versorgungsprozesse auf horizontaler und vertikaler Ebe-ne werden Wirtschaftlichkeits- und Effektivitätsparameter für ein besseres Angebot gesundheitsbezogener Dienstleistungen und Produkte herausgestellt und Koordinati-ons-, Kooperations- und Kommunikationsprozesse verbessert. Bisher hat das GKV-Modernisierungsgesetz die Umsetzung dieser innovativen Ver-sorgungsform und die damit verbundenen Wettbewerbsanreize zwar vorangetrieben, doch wurden der gesetzliche Rahmen und die Gestaltungsfreiheit noch nicht in vol-lem Umfang genutzt. Im Sommer 2005 führte die Hochschule Neubrandenburg in Kooperation mit dem Berliner Zentrum Public Health und der Gesellschaft für empirische Beratung mbH eine Studie zum Umsetzungsstand der Integrierten Versorgung nach §§140a-d SGB V durch. Neben der Erhebung des Status Quo mit Bezug auf die geschichtliche Ent-wicklung sowie die Manifestierung innovativer Versorgungsstrukturen in Deutsch-land bestand das Ziel der empirischen Erhebung auch darin, Aufschlüsse über Mei-nungen und Bewertungen der verschiedenen Leistungserbringer zu erhalten. Ziele und Ansätze der Integrierten Versorgung, gesetzliche Rahmenbedingungen und das auf dieser Grundlage basierende Vertragsgeschehen sowie die Möglichkeiten der Finanzierung finden in dieser Untersuchung weitere Beachtung. Im Folgenden werden die Studienergebnisse in ihrer theoretischen und praktischen Analyse in Bezug auf die Umsetzung und den Versorgungsumfang zum Erhebungs-zeitpunkt (Juli 2005) dargestellt. Die Ergebnisse können als Vergleichsgrundlage für zukünftige Erhebungen – nach Ausgestaltung der in der Gesundheitsreform geplan-ten Maßnahmen zur Stärkung der IV – angesehen werden."[Autorenreferat]"In international comparisons the German Health Care System is classified as a sys-tem of high quality standards in supply chain. Nevertheless, there is a political failure in optimal allocation of existing financial resources. Politicians are often confronted with the current problem to reform the health system regarding possible savings and economical potential. Federal government for instance attempt to solve such serious problems bringing out the Eckpunktepapier in July 2006. Getting out of the financial crisis the Eckpunktepapier could not give the right answer, but unmet expectations do not lead to reasons of desperation because otherwise the health system has many organisational possibilities. In this case measures to strengthen the integrated deliv-ery of care are very important. Integration means both horizontal and vertical level of integration to optimize efficiency and effectiveness of health products and services, but not least the process of coordination, cooperation and communication in health supply. While the implementation of innovative structure in health care including its incentives to competition expend, the legal framework which offers further possibili-ties of optimization is not totally used by health organizations at time. In the summer 2005 the University of Neubrandenburg accomplished a study in co-operation with the public health centre of Berlin and the Association for empirical consultation GmbH. The study’s aim was to analyse the conversion conditions of the integrated health care based on §§ 140a-d SGB V. Apart from the collection of the status quo with reference to the historical development as well as the manifestation of innovative supplying structures in Germany the ambition of the empirical collec-tion consisted also of receiving explanations about opinions and evaluations of the institutions and persons who furnish the health achievements. Ambitions and begin-nings of the integrated health care, the legal framework and the contract happening as well as the possibilities of the financing receive further attention in this study. In the following the theoretical and practical study results are represented. They ana-lyse the conversion and the extent of the integrated health care at the collection time (July 2005). These results can be regarded as comparison basis for other studies in the future - after measures planned in the health reform will be converted for the sta-bilization of the integrated health care."[author's abstract

Heisenberg's Uncertainty Relation and Bell Inequalities in High Energy Physics

An effective formalism is developed to handle decaying two-state systems. Herewith, observables of such systems can be described by a single operator in the Heisenberg picture. This allows for using the usual framework in quantum information theory and, hence, to enlighten the quantum feature of such systems compared to non-decaying systems. We apply it to systems in high energy physics, i.e. to oscillating meson-antimeson systems. In particular, we discuss the entropic Heisenberg uncertainty relation for observables measured at different times at accelerator facilities including the effect of CP violation, i.e. the imbalance of matter and antimatter. An operator-form of Bell inequalities for systems in high energy physics is presented, i.e. a Bell-witness operator, which allows for simple analysis of unstable systems.Comment: 17 page

Credit Risk Meets Random Matrices: Coping with Non-Stationary Asset Correlations

We review recent progress in modeling credit risk for correlated assets. We employ a new interpretation of the Wishart model for random correlation matrices to model non-stationary effects. We then use the Merton model in which default events and losses are derived from the asset values at maturity. To estimate the time development of the asset values, the stock prices are used, the correlations of which have a strong impact on the loss distribution, particularly on its tails. These correlations are non-stationary, which also influences the tails. We account for the asset fluctuations by averaging over an ensemble of random matrices that models the truly existing set of measured correlation matrices. As a most welcome side effect, this approach drastically reduces the parameter dependence of the loss distribution, allowing us to obtain very explicit results, which show quantitatively that the heavy tails prevail over diversification benefits even for small correlations. We calibrate our random matrix model with market data and show how it is capable of grasping different market situations. Furthermore, we present numerical simulations for concurrent portfolio risks, i.e., for the joint probability densities of losses for two portfolios. For the convenience of the reader, we give an introduction to the Wishart random matrix model

Extreme Portfolio Loss Correlations in Credit Risk

The stability of the financial system is associated with systemic risk factors such as the concurrent default of numerous small obligors. Hence, it is of utmost importance to study the mutual dependence of losses for different creditors in the case of large, overlapping credit portfolios. We analytically calculate the multivariate joint loss distribution of several credit portfolios on a non-stationary market. To take fluctuating asset correlations into account, we use an random matrix approach which preserves, as a much appreciated side effect, analytical tractability and drastically reduces the number of parameters. We show that, for two disjoint credit portfolios, diversification does not work in a correlated market. Additionally, we find large concurrent portfolio losses to be rather likely. We show that significant correlations of the losses emerge not only for large portfolios with thousands of credit contracts, but also for small portfolios consisting of a few credit contracts only. Furthermore, we include subordination levels, which were established in collateralized debt obligations to protect the more senior tranches from high losses. We analytically corroborate the observation that an extreme loss of the subordinated creditor is likely to also yield a large loss of the senior creditor

Nano-Indentation to Determine Mechanical Properties of Intraocular Lenses: Evaluating Penetration Depth, Material Stiffness, and Elastic Moduli

Abstract Introduction Intraocular lenses (IOL) should remain in the eye for life after implantation into the capsular bag during cataract surgery. The material must meet various requirements. It is crucial that the material has the best biocompatibility, and it should be flexible and soft for best possible implantation process but also sufficiently stable and stiff for good centering in the eye and posterior capsule opacification prevention. Methods In this laboratory experiment, we used nano-indentation for the mechanical assessment of three hydrophobic acrylic (A, B, C), three hydrophilic acrylic (D, E, F), and one silicone (G) intraocular lens. We wanted to determine whether some react more sensitively to touching/handling than others. The indentation elastic modulus and the creep were obtained from the force displacement curve. For measuring penetration depth and testing of possible damage to the intraocular lenses, the samples were measured at room temperature. A 200-µm-diameter ruby spherical tipped indenter was used for all the tests. Indentations were made to three different maximum loads, namely 5 mN (milli Newton), 15 mN, and 30 mN and repeated three times. Results The lowest penetration depth (12 µm) was observed with IOL B. However, IOL A, D, and F showed similar low penetration depths (20, 18, and 23 µm, respectively). Lenses C and E showed slightly higher penetration depths of 36 and 39 µm, respectively. The silicone lens (G) showed the greatest penetration depth of 54.6 µm at a maximum load of 5 mN. With higher maximal loads (15 and 30 mN) the penetration depth increased significantly. Lens C, however, showed the same results at both 15 and 30 mN with no increase of penetration depth. This seems to fit well with the material and manufacturing process of the lens (lathe-cut). During the holding time of 30 s at constant force all six acrylic lenses showed a significant increase of the creep (C IT 21–43%). Lens G showed the smallest creep with 14%. The mean indentation modulus (E IT) values ranged from 1 to 37 MPa. IOL B had the largest E IT of 37 MPa, which could be caused by the low water content. Conclusion It was found that results correlate very well with the water content of the material in the first place. The manufacturing process (molded versus lathe-cut) seems to play another important role. Since all included acrylic lenses are very similar, it was not surprising that the measured differences are marginal. Even though hydrophobic materials with lower water content showed higher relative stiffness, penetration and defects can also occur with these. The surgeon and scrub nurse should always be aware that macroscopic changes are difficult to detect but that defects could theoretically lead to clinical effects. The principle of not touching the center of the IOL optic at any time should be taken seriously