Risikomaße in der Finanzmathematik

„Risikomaße in der Finanzmathematik“ Der Value-at -Risk (VaR) ist ein Risikomaß, dessen Verwendung von der Bankenaufsicht gefordert wird. Der Vorteil des VaR liegt – als Quantil der Ertrags- oder Verlustverteilung - vor allem in seiner einfachen Interpretierbarkeit. Nachteilig ist, dass der linke Rand der Wahrscheinlichkeitsverteilung nicht beachtet wird. Darüber hinaus ist die Berechnung des VaR schwierig, da Quantile nicht additiv sind. Der größte Nachteil des VaR ist in der fehlenden Subadditivität zu sehen. Deswegen werden Alternativen wie Expected Shortfall untersucht. In dieser Arbeit werden zunächst finanzielle Risikomaße eingeführt und einige ihre grundlegenden Eigenschaften festgehalten. Wir beschäftigen uns mit verschiedenen parametrischen und nichtparametrischen Methoden zur Ermittlung des VaR, unter anderen mit ihren Vorteilen und Nachteilen. Des Weiteren beschäftigen wir uns mit parametrischen und nichtparametrischen Schätzern vom VaR in diskreter Zeit. Wir stellen Portfoliooptimierungsprobleme im Black Scholes Modell mit beschränktem VaR und mit beschränkter Varianz vor. Der Vorteil des erstens Ansatzes gegenüber dem zweiten wird hier erläutert. Wir lösen Nutzenoptimierungsprobleme in Bezug auf das Endvermögen mit beschränktem VaR und mit beschränkter Varianz. VaR sagt nichts über den darüber hinausgehenden Verlust aus, während dieser von Expected Shortfall berücksichtigt wird. Deswegen verwenden wir hier den Expected Shortfall anstelle des von Emmer, Korn und Klüppelberg (2001) betrachteten Risikomaßes VaR für die Optimierung des Portfolios im Black Scholes Modell.

A picture is worth a thousand words--the utility of 3D visualization illustrated by a case of survived pancreatic transection

It is one of the most important tasks of the forensic pathologist to explain the forensically relevant medical findings to medical non-professionals. However, it is often difficult to comment on the nature and potential consequences of organ injuries in a comprehensive way to individuals with limited knowledge of anatomy and physiology. This rare case of survived pancreatic transaction after kicks to the abdomen illustrates how the application of dedicated software programs for three-dimensional reconstruction can overcome these difficulties, allowing for clear and concise visualization of complex findings.

Fully Automatic Segmentation of Brain Tumor Images using Support Vector Machine Classiffication in Combination with Hierarchical Conditional Random Field Regularization

Delineating brain tumor boundaries from magnetic resonance images is an essential task for the analysis of brain cancer. We propose a fully automatic method for brain tissue segmentation, which combines Support Vector Machine classification using multispectral intensities and textures with subsequent hierarchical regularization based on Conditional Random Fields. The CRF regularization introduces spatial constraints to the powerful SVM classification, which assumes voxels to be independent from their neighbors. The approach first separates healthy and tumor tissue before both regions are subclassified into cerebrospinal fluid, white matter, gray matter and necrotic, active, edema region respectively in a novel hierarchical way. The hierarchical approach adds robustness and speed by allowing to apply different levels of regularization at different stages. The method is fast and tailored to standard clinical acquisition protocols. It was assessed on 10 multispectral patient datasets with results outperforming previous methods in terms of segmentation detail and computation times.

The prognostic utility of the SYNTAX score on 1-year outcomes after revascularization with zotarolimus- and everolimus-eluting stents: a substudy of the RESOLUTE All Comers Trial

This study assessed the ability of the SYNTAX score (SXscore) to stratify risk in patients treated with percutaneous coronary intervention (PCI) using zotarolimus-eluting or everolimus-eluting stents.

Electroencephalographic topography measures of experienced utility

Economic theory distinguishes two concepts of utility: decision utility, objectively quantifiable by choices, and experienced utility, referring to the satisfaction by an obtainment. To date, experienced utility is typically measured with subjective ratings. This study intended to quantify experienced utility by global levels of neuronal activity. Neuronal activity was measured by means of electroencephalographic (EEG) responses to gain and omission of graded monetary rewards at the level of the EEG topography in human subjects. A novel analysis approach allowed approximating psychophysiological value functions for the experienced utility of monetary rewards. In addition, we identified the time windows of the event-related potentials (ERP) and the respective intracortical sources, in which variations in neuronal activity were significantly related to the value or valence of outcomes. Results indicate that value functions of experienced utility and regret disproportionally increase with monetary value, and thus contradict the compressing value functions of decision utility. The temporal pattern of outcome evaluation suggests an initial (∼250 ms) coarse evaluation regarding the valence, concurrent with a finer-grained evaluation of the value of gained rewards, whereas the evaluation of the value of omitted rewards emerges later. We hypothesize that this temporal double dissociation is explained by reward prediction errors. Finally, a late, yet unreported, reward-sensitive ERP topography (∼500 ms) was identified. The sources of these topographical covariations are estimated in the ventromedial prefrontal cortex, the medial frontal gyrus, the anterior and posterior cingulate cortex and the hippocampus/amygdala. The results provide important new evidence regarding “how,” “when,” and “where” the brain evaluates outcomes with different hedonic impact.

Predicting future risk of asthma exacerbations using individual conditional probabilities

Determination of future risk of exacerbations is a key issue in the management of asthma. We previously developed a method to calculate conditional probabilities (π) of future decreases in lung function by using the daily fluctuations in peak expiratory flow (PEF).