A general framework for multi-compartmental analysis of drug chemotherapy dynamics in human immunodeficiency virus type-1 infected individuals

An optimal control strategy for the highly active antiretroviral therapy associated to the acquired immunodeficiency syndrome should be designed regarding a comprehensive analysis of the drug chemotherapy behavior in the host tissues, from major viral replication sites to viral sanctuary compartments. Such approach is critical in order to efficiently explore synergistic, competitive and prohibitive relationships among drugs and, hence, therapy costs and side-effect minimization. In this paper, a novel mathematical model for HIV-1 drug chemotherapy dynamics in distinct host anatomic compartments is proposed and theoretically evaluated on fifteen conventional anti-retroviral drugs. Rather than interdependence between drug type and its concentration profile in a host tissue, simulated results suggest that such profile is importantly correlated with the host tissue under consideration. Furthermore, the drug accumulative dynamics are drastically affected by low patient compliance with pharmacotherapy, even when a single dose lacks. (C) 2012 Elsevier Inc. All rights reserved.

Arbitrage-Free Conditions and Hedging Strategies for Markets with Penalty Costs on Short Positions

We consider a discrete-time financial model in a general sample space with penalty costs on short positions. We consider a friction market closely related to the standard one except that withdrawals from the portfolio value proportional to short positions are made. We provide necessary and sufficient conditions for the nonexistence of arbitrages in this situation and for a self-financing strategy to replicate a contingent claim. For the finite-sample space case, this result leads to an explicit and constructive procedure for obtaining perfect hedging strategies.

Integrodifference model for blowfly invasion

We propose a stage-structured integrodifference model for blowflies' growth and dispersion taking into account the density dependence of fertility and survival rates and the non-overlap of generations. We assume a discrete-time, stage-structured, model. The spatial dynamics is introduced by means of a redistribution kernel. We treat one and two dimensional cases, the latter on the semi-plane, with a reflexive boundary. We analytically show that the upper bound for the invasion front speed is the same as in the one-dimensional case. Using laboratory data for fertility and survival parameters and dispersal data of a single generation from a capture-recapture experiment in South Africa, we obtain an estimate for the velocity of invasion of blowflies of the species Chrysomya albiceps. This model predicts a speed of invasion which was compared to actual observational data for the invasion of the focal species in the Neotropics. Good agreement was found between model and observations.

A combined oral contraceptive containing drospirenone changes neither endothelial function nor hemodynamic parameters in healthy young women: a prospective clinical trial

Background: Combined oral contraceptives (COCs) may lead to a rise in cardiovascular disease risk, possibly associated with changes in blood pressure and endothelial function. Study Design: The objective was to evaluate the impact of COC containing 20 mcg of ethinylestradiol (EE) and 3 mg of drospirenone (DRSP) on the arterial endothelial function, systolic and diastolic blood pressure (SBP and DBP, respectively), heart rate (HR), cardiac output (CO) and total peripheral resistance (TPR) of healthy young women. Of the 71 women in the study, 43 were evaluated before the introduction of COC and after 6 months of its use (case group) and 28, COC nonusers, were assessed for the same parameters at the same time interval (control group). Results: No significant changes in endothelium-dependent and endothelium-independent functions or in measures of SBP, DBP, HR, CO and TPR caused by COC use were observed in the case group (p>.05 for all variables) or in the control group. Conclusion: These data suggest COC with 20 mcg EE and 3 mg DRSP does not alter arterial endothelial function or hemodynamic parameters in healthy young women. (C) 2012 Elsevier Inc. All rights reserved.

Combinatorial-topological framework for the analysis of global dynamics

We discuss an algorithmic framework based on efficient graph algorithms and algebraic-topological computational tools. The framework is aimed at automatic computation of a database of global dynamics of a given m-parameter semidynamical system with discrete time on a bounded subset of the n-dimensional phase space. We introduce the mathematical background, which is based upon Conley's topological approach to dynamics, describe the algorithms for the analysis of the dynamics using rectangular grids both in phase space and parameter space, and show two sample applications. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4767672]

The rapid atmospheric monitoring system of the Pierre Auger Observatory

The Pierre Auger Observatory is a facility built to detect air showers produced by cosmic rays above 10(17) eV. During clear nights with a low illuminated moon fraction, the UV fluorescence light produced by air showers is recorded by optical telescopes at the Observatory. To correct the observations for variations in atmospheric conditions, atmospheric monitoring is performed at regular intervals ranging from several minutes (for cloud identification) to several hours (for aerosol conditions) to several days (for vertical profiles of temperature, pressure, and humidity). In 2009, the monitoring program was upgraded to allow for additional targeted measurements of atmospheric conditions shortly after the detection of air showers of special interest, e. g., showers produced by very high-energy cosmic rays or showers with atypical longitudinal profiles. The former events are of particular importance for the determination of the energy scale of the Observatory, and the latter are characteristic of unusual air shower physics or exotic primary particle types. The purpose of targeted (or "rapid") monitoring is to improve the resolution of the atmospheric measurements for such events. In this paper, we report on the implementation of the rapid monitoring program and its current status. The rapid monitoring data have been analyzed and applied to the reconstruction of air showers of high interest, and indicate that the air fluorescence measurements affected by clouds and aerosols are effectively corrected using measurements from the regular atmospheric monitoring program. We find that the rapid monitoring program has potential for supporting dedicated physics analyses beyond the standard event reconstruction.

Inhibition of Macrophage Oxidative Stress Prevents the Reduction of ABCA-1 Transporter Induced by Advanced Glycated Albumin

We investigated the role of aminoguanidine and benfotiamine on the inhibition of reactive oxygen species (ROS) generation in macrophages induced by advanced glycated albumin (AGE-albumin) and its relationship with cell cholesterol homeostasis, emphasizing the expression of the ATP binding cassette transporter A-1 (ABCA-1). AGE-albumin was made by incubating fatty acid-free albumin with 10 mM glycolaldehyde. ROS production and ABCA-1 protein level were determined by flow cytometry in J774 macrophages treated along time with control (C) or AGE-albumin alone or in the presence of aminoguanidine or benfotiamine. Mitochondrial function was evaluated by oxygraphy. Compared to C-albumin, AGE-albumin increased ROS production in macrophages, which was ascribed to the activities of NADPH oxidase and of the mitochondrial system. Mitochondrial respiratory chain activity was reduced in cells incubated with AGE-albumin. ROS generation along time was associated with the reduction in macrophage ABCA-1 protein level. Aminoguanidine prevented ROS elevation and restored the ABCA-1 content in macrophages; on the other hand, benfotiamine that promoted a lesser reduction in ROS generation was not able to restore ABCA-1 levels. Inhibition of oxidative stress induced by AGE-albumin prevents disturbances in reverse cholesterol transport by curbing the reduction of ABCA-1 elicited by advanced glycation in macrophages and therefore may contribute to the prevention of atherosclerosis in diabetes mellitus.

Management of diabetes mellitus and associated cardiovascular risk factors in Brazil – the Brazilian study on the practice of diabetes care

Abstract Background The Brazilian Study on the Practice of Diabetes Care main objective was to provide an epidemiological profile of individuals with type 1 and 2 diabetes mellitus (DM) in Brazil, concerning therapy and adherence to international guidelines in the medical practice. Methods This observational, cross-sectional, multicenter study collected and analyzed data from individuals with type 1 and 2 DM attending public or private clinics in Brazil. Each investigator included the first 10 patients with type 2 DM who visited his/her office, and the first 5 patients with type 1 DM. Results A total of 1,358 patients were analyzed; 375 (27.6%) had type 1 and 983 (72.4%) had type 2 DM. Most individuals were women, Caucasian, and private health care users. High prevalence rates of hypertension, dyslipidemia and central obesity were observed, particularly in type 2 DM. Only 7.3% and 5.1% of the individuals with types 1 and 2 DM, respectively, had optimal control of blood pressure, plasma glucose and lipids. The absence of hypertension and female sex were associated with better control of type 1 DM and other cardiovascular risk factors. In type 2 DM, older age was also associated with better control. Conclusions Female sex, older age, and absence of hypertension were associated with better metabolic control. An optimal control of plasma glucose and other cardiovascular risk factors are obtained only in a minority of individuals with diabetes. Local numbers, compared to those from other countries are worse.

Spectrum shaping and its application: spread-spectrum clock generator and circuits for ultra wide band

Electromagnetic spectrum can be identified as a resource for the designer, as well as for the manufacturer, from two complementary points of view: first, because it is a good in great demand by many different kind of applications; second, because despite its scarce availability, it may be advantageous to use more spectrum than necessary. This is the case of Spread-Spectrum Systems, those systems in which the transmitted signal is spread over a wide frequency band, much wider, in fact, than the minimum bandwidth required to transmit the information being sent. Part I of this dissertation deals with Spread-Spectrum Clock Generators (SSCG) aiming at reducing Electro Magnetic Interference (EMI) of clock signals in integrated circuits (IC) design. In particular, the modulation of the clock and the consequent spreading of its spectrum are obtained through a random modulating signal outputted by a chaotic map, i.e. a discrete-time dynamical system showing chaotic behavior. The advantages offered by this kind of modulation are highlighted. Three different prototypes of chaos-based SSCG are presented in all their aspects: design, simulation, and post-fabrication measurements. The third one, operating at a frequency equal to 3GHz, aims at being applied to Serial ATA, standard de facto for fast data transmission to and from Hard Disk Drives. The most extreme example of spread-spectrum signalling is the emerging ultra-wideband (UWB) technology, which proposes the use of large sections of the radio spectrum at low amplitudes to transmit high-bandwidth digital data. In part II of the dissertation, two UWB applications are presented, both dealing with the advantages as well as with the challenges of a wide-band system, namely: a chaos-based sequence generation method for reducing Multiple Access Interference (MAI) in Direct Sequence UWB Wireless-Sensor-Networks (WSNs), and design and simulations of a Low-Noise Amplifier (LNA) for impulse radio UWB. This latter topic was studied during a study-abroad period in collaboration with Delft University of Technology, Delft, Netherlands.

Enabling Blocks for Integrated CMOS UWB Transceivers

The last decades have seen an unrivaled growth and diffusion of mobile telecommunications. Several standards have been developed to this purposes, from GSM mobile phone communications to WLAN IEEE 802.11, providing different services for the the transmission of signals ranging from voice to high data rate digital communications and Digital Video Broadcasting (DVB). In this wide research and market field, this thesis focuses on Ultra Wideband (UWB) communications, an emerging technology for providing very high data rate transmissions over very short distances. In particular the presented research deals with the circuit design of enabling blocks for MB-OFDM UWB CMOS single-chip transceivers, namely the frequency synthesizer and the transmission mixer and power amplifier. First we discuss three different models for the simulation of chargepump phase-locked loops, namely the continuous time s-domain and discrete time z-domain approximations and the exact semi-analytical time-domain model. The limitations of the two approximated models are analyzed in terms of error in the computed settling time as a function of loop parameters, deriving practical conditions under which the different models are reliable for fast settling PLLs up to fourth order. Besides, a phase noise analysis method based upon the time-domain model is introduced and compared to the results obtained by means of the s-domain model. We compare the three models over the simulation of a fast switching PLL to be integrated in a frequency synthesizer for WiMedia MB-OFDM UWB systems. In the second part, the theoretical analysis is applied to the design of a 60mW 3.4 to 9.2GHz 12 Bands frequency synthesizer for MB-OFDM UWB based on two wide-band PLLs. The design is presented and discussed up to layout level. A test chip has been implemented in TSMC CMOS 90nm technology, measured data is provided. The functionality of the circuit is proved and specifications are met with state-of-the-art area occupation and power consumption. The last part of the thesis deals with the design of a transmission mixer and a power amplifier for MB-OFDM UWB band group 1. The design has been carried on up to layout level in ST Microlectronics 65nm CMOS technology. Main characteristics of the systems are the wideband behavior (1.6 GHz of bandwidth) and the constant behavior over process parameters, temperature and supply voltage thanks to the design of dedicated adaptive biasing circuits.

Black-scholes type equations

In this work we are concerned with the analysis and numerical solution of Black-Scholes type equations arising in the modeling of incomplete financial markets and an inverse problem of determining the local volatility function in a generalized Black-Scholes model from observed option prices. In the first chapter a fully nonlinear Black-Scholes equation which models transaction costs arising in option pricing is discretized by a new high order compact scheme. The compact scheme is proved to be unconditionally stable and non-oscillatory and is very efficient compared to classical schemes. Moreover, it is shown that the finite difference solution converges locally uniformly to the unique viscosity solution of the continuous equation. In the next chapter we turn to the calibration problem of computing local volatility functions from market data in a generalized Black-Scholes setting. We follow an optimal control approach in a Lagrangian framework. We show the existence of a global solution and study first- and second-order optimality conditions. Furthermore, we propose an algorithm that is based on a globalized sequential quadratic programming method and a primal-dual active set strategy, and present numerical results. In the last chapter we consider a quasilinear parabolic equation with quadratic gradient terms, which arises in the modeling of an optimal portfolio in incomplete markets. The existence of weak solutions is shown by considering a sequence of approximate solutions. The main difficulty of the proof is to infer the strong convergence of the sequence. Furthermore, we prove the uniqueness of weak solutions under a smallness condition on the derivatives of the covariance matrices with respect to the solution, but without additional regularity assumptions on the solution. The results are illustrated by a numerical example.

Untersuchung zur Bestimmung quantitativer Parameter der Lungenventilation mittels CT und MRT

Die zuverlässige Berechnung von quantitativen Parametern der Lungenventilation ist für ein Verständnis des Verhaltens der Lunge und insbesondere für die Diagnostik von Lungenerkrankungen von großer Bedeutung. Nur durch quantitative Parameter sind verlässliche und reproduzierbare diagnostische Aussagen über den Gesundheitszustand der Lunge möglich. Im Rahmen dieser Arbeit wurden neue quantitative Verfahren zur Erfassung der Lungenventilation basierend auf der dynamischen Computer- (CT) und Magnetresonanztomographie (MRT) entwickelt. Im ersten Teil dieser Arbeit wurde die Frage untersucht, ob das Aufblähen der Lunge in gesunden Schweinelungen und Lungen mit Akutem Lungenversagen (ARDS) durch einzelne, diskrete Zeitkonstanten beschrieben werden kann, oder ob kontinuierliche Verteilungen von Zeitkonstanten die Realität besser beschreiben. Hierzu wurden Serien dynamischer CT-Aufnahmen während definierter Beatmungsmanöver (Drucksprünge) aufgenommen und anschließend aus den Messdaten mittels inverser Laplace-Transformation die zugehörigen Verteilungen der Zeitkonstanten berechnet. Um die Qualität der Ergebnisse zu analysieren, wurde der Algorithmus im Rahmen von Simulationsrechnungen systematisch untersucht und anschließend in-vivo an gesunden und ARDS-Schweinelungen eingesetzt. Während in den gesunden Lungen mono- und biexponentielle Verteilungen bestimmt wurden, waren in den ARDS-Lungen Verteilungen um zwei dominante Zeitkonstanten notwendig, um die gemessenen Daten auf der Basis des verwendeten Modells verlässlich zu beschreiben. Es wurden sowohl diskrete als auch kontinuierliche Verteilungen gefunden. Die CT liefert Informationen über das solide Lungengewebe, während die MRT von hyperpolarisiertem 3He in der Lage ist, direkt das eingeatmete Gas abzubilden. Im zweiten Teil der Arbeit wurde zeitlich hochaufgelöst das Einströmen eines 3He-Bolus in die Lunge erfasst. Über eine Entfaltungsanalyse wurde anschließend das Einströmverhalten unter Idealbedingungen (unendlich kurzer 3He-Bolus), also die Gewebeantwortfunktion, berechnet und so eine Messtechnik-unabhängige Erfassung des Einströmens von 3He in die Lunge ermöglicht. Zentrale Fragestellung war hier, wie schnell das Gas in die Lunge einströmt. Im Rahmen von Simulationsrechnungen wurde das Verhalten eines Entfaltungsalgorithmus (basierend auf B-Spline Repräsentationen) systematisch analysiert. Zusätzlich wurde ein iteratives Entfaltungsverfahren eingesetzt. Aus zeitlich hochaufgelösten Messungen (7ms) an einer gesunden und einer ARDS-Schweinelunge konnte erstmals nachgewiesen werden, dass das Einströmen in-vivo in weniger als 0,1s geschieht. Die Ergebnisse zeigen Zeitkonstanten im Bereich von 4ms–50ms, wobei zwischen der gesunden Lungen und der ARDS-Lunge deutliche Unterschiede beobachtet wurden. Zusammenfassend ermöglichen daher die in dieser Arbeit vorgestellten Algorithmen eine objektivere Bestimmung quantitativer Parameter der Lungenventilation. Dies ist für die eindeutige Beschreibung ventilatorischer Vorgänge in der Lunge und somit für die Lungendiagnostik unerlässlich. Damit stehen quantitative Methoden für die Lungenfunktionsdiagnostik zur Verfügung, deren diagnostische Relevanz im Rahmen wissenschaftlicher und klinischer Studien untersucht werden kann.

Advanced CMOS Interfaces for Bio-Nanosensors

The improvement of devices provided by Nanotechnology has put forward new classes of sensors, called bio-nanosensors, which are very promising for the detection of biochemical molecules in a large variety of applications. Their use in lab-on-a-chip could gives rise to new opportunities in many fields, from health-care and bio-warfare to environmental and high-throughput screening for pharmaceutical industry. Bio-nanosensors have great advantages in terms of cost, performance, and parallelization. Indeed, they require very low quantities of reagents and improve the overall signal-to-noise-ratio due to increase of binding signal variations vs. area and reduction of stray capacitances. Additionally, they give rise to new challenges, such as the need to design high-performance low-noise integrated electronic interfaces. This thesis is related to the design of high-performance advanced CMOS interfaces for electrochemical bio-nanosensors. The main focus of the thesis is: 1) critical analysis of noise in sensing interfaces, 2) devising new techniques for noise reduction in discrete-time approaches, 3) developing new architectures for low-noise, low-power sensing interfaces. The manuscript reports a multi-project activity focusing on low-noise design and presents two developed integrated circuits (ICs) as examples of advanced CMOS interfaces for bio-nanosensors. The first project concerns low-noise current-sensing interface for DC and transient measurements of electrophysiological signals. The focus of this research activity is on the noise optimization of the electronic interface. A new noise reduction technique has been developed so as to realize an integrated CMOS interfaces with performance comparable with state-of-the-art instrumentations. The second project intends to realize a stand-alone, high-accuracy electrochemical impedance spectroscopy interface. The system is tailored for conductivity-temperature-depth sensors in environmental applications, as well as for bio-nanosensors. It is based on a band-pass delta-sigma technique and combines low-noise performance with low-power requirements.

Reinforcement Lernen mit Regularisierungsnetzwerken

Die Arbeit behandelt das Problem der Skalierbarkeit von Reinforcement Lernen auf hochdimensionale und komplexe Aufgabenstellungen. Unter Reinforcement Lernen versteht man dabei eine auf approximativem Dynamischen Programmieren basierende Klasse von Lernverfahren, die speziell Anwendung in der Künstlichen Intelligenz findet und zur autonomen Steuerung simulierter Agenten oder realer Hardwareroboter in dynamischen und unwägbaren Umwelten genutzt werden kann. Dazu wird mittels Regression aus Stichproben eine Funktion bestimmt, die die Lösung einer "Optimalitätsgleichung" (Bellman) ist und aus der sich näherungsweise optimale Entscheidungen ableiten lassen. Eine große Hürde stellt dabei die Dimensionalität des Zustandsraums dar, die häufig hoch und daher traditionellen gitterbasierten Approximationsverfahren wenig zugänglich ist. Das Ziel dieser Arbeit ist es, Reinforcement Lernen durch nichtparametrisierte Funktionsapproximation (genauer, Regularisierungsnetze) auf -- im Prinzip beliebig -- hochdimensionale Probleme anwendbar zu machen. Regularisierungsnetze sind eine Verallgemeinerung von gewöhnlichen Basisfunktionsnetzen, die die gesuchte Lösung durch die Daten parametrisieren, wodurch die explizite Wahl von Knoten/Basisfunktionen entfällt und so bei hochdimensionalen Eingaben der "Fluch der Dimension" umgangen werden kann. Gleichzeitig sind Regularisierungsnetze aber auch lineare Approximatoren, die technisch einfach handhabbar sind und für die die bestehenden Konvergenzaussagen von Reinforcement Lernen Gültigkeit behalten (anders als etwa bei Feed-Forward Neuronalen Netzen). Allen diesen theoretischen Vorteilen gegenüber steht allerdings ein sehr praktisches Problem: der Rechenaufwand bei der Verwendung von Regularisierungsnetzen skaliert von Natur aus wie O(n**3), wobei n die Anzahl der Daten ist. Das ist besonders deswegen problematisch, weil bei Reinforcement Lernen der Lernprozeß online erfolgt -- die Stichproben werden von einem Agenten/Roboter erzeugt, während er mit der Umwelt interagiert. Anpassungen an der Lösung müssen daher sofort und mit wenig Rechenaufwand vorgenommen werden. Der Beitrag dieser Arbeit gliedert sich daher in zwei Teile: Im ersten Teil der Arbeit formulieren wir für Regularisierungsnetze einen effizienten Lernalgorithmus zum Lösen allgemeiner Regressionsaufgaben, der speziell auf die Anforderungen von Online-Lernen zugeschnitten ist. Unser Ansatz basiert auf der Vorgehensweise von Recursive Least-Squares, kann aber mit konstantem Zeitaufwand nicht nur neue Daten sondern auch neue Basisfunktionen in das bestehende Modell einfügen. Ermöglicht wird das durch die "Subset of Regressors" Approximation, wodurch der Kern durch eine stark reduzierte Auswahl von Trainingsdaten approximiert wird, und einer gierigen Auswahlwahlprozedur, die diese Basiselemente direkt aus dem Datenstrom zur Laufzeit selektiert. Im zweiten Teil übertragen wir diesen Algorithmus auf approximative Politik-Evaluation mittels Least-Squares basiertem Temporal-Difference Lernen, und integrieren diesen Baustein in ein Gesamtsystem zum autonomen Lernen von optimalem Verhalten. Insgesamt entwickeln wir ein in hohem Maße dateneffizientes Verfahren, das insbesondere für Lernprobleme aus der Robotik mit kontinuierlichen und hochdimensionalen Zustandsräumen sowie stochastischen Zustandsübergängen geeignet ist. Dabei sind wir nicht auf ein Modell der Umwelt angewiesen, arbeiten weitestgehend unabhängig von der Dimension des Zustandsraums, erzielen Konvergenz bereits mit relativ wenigen Agent-Umwelt Interaktionen, und können dank des effizienten Online-Algorithmus auch im Kontext zeitkritischer Echtzeitanwendungen operieren. Wir demonstrieren die Leistungsfähigkeit unseres Ansatzes anhand von zwei realistischen und komplexen Anwendungsbeispielen: dem Problem RoboCup-Keepaway, sowie der Steuerung eines (simulierten) Oktopus-Tentakels.

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.