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.

Wavelet estimation in diffusions with periodicity

Wir betrachten einen zeitlich inhomogenen Diffusionsprozess, der durch eine stochastische Differentialgleichung gegeben wird, deren Driftterm ein deterministisches T-periodisches Signal beinhaltet, dessen Periodizität bekannt ist. Dieses Signal sei in einem Besovraum enthalten. Wir schätzen es mit Hilfe eines nichtparametrischen Waveletschätzers. Unser Schätzer ist von einem Wavelet-Dichteschätzer mit Thresholding inspiriert, der 1996 in einem klassischen iid-Modell von Donoho, Johnstone, Kerkyacharian und Picard konstruiert wurde. Unter gewissen Ergodizitätsvoraussetzungen an den Prozess können wir nichtparametrische Konvergenzraten angegeben, die bis auf einen logarithmischen Term den Raten im klassischen iid-Fall entsprechen. Diese Raten werden mit Hilfe von Orakel-Ungleichungen gezeigt, die auf Ergebnissen über Markovketten in diskreter Zeit von Clémencon, 2001, beruhen. Außerdem betrachten wir einen technisch einfacheren Spezialfall und zeigen einige Computersimulationen dieses Schätzers.

Stationary states in random walks on networks

In this thesis we dealt with the problem of describing a transportation network in which the objects in movement were subject to both finite transportation capacity and finite accomodation capacity. The movements across such a system are realistically of a simultaneous nature which poses some challenges when formulating a mathematical description. We tried to derive such a general modellization from one posed on a simplified problem based on asyncronicity in particle transitions. We did so considering one-step processes based on the assumption that the system could be describable through discrete time Markov processes with finite state space. After describing the pre-established dynamics in terms of master equations we determined stationary states for the considered processes. Numerical simulations then led to the conclusion that a general system naturally evolves toward a congestion state when its particle transition simultaneously and we consider one single constraint in the form of network node capacity. Moreover the congested nodes of a system tend to be located in adjacent spots in the network, thus forming local clusters of congested nodes.

Prognostic importance of anaemia in patients with acute pulmonary embolism

Although associated with adverse outcomes in other cardiopulmonary diseases, limited evidence exists on the prognostic value of anaemia in patients with acute pulmonary embolism (PE). We sought to examine the associations between anaemia and mortality and length of hospital stay in patients with PE. We evaluated 14,276 patients with a primary diagnosis of PE from 186 hospitals in Pennsylvania, USA. We used random-intercept logistic regression to assess the association between anaemia at the time of presentation and 30-day mortality and discrete-time logistic hazard models to assess the association between anaemia and time to hospital discharge, adjusting for patient (age, gender, race, insurance type, clinical and laboratory variables) and hospital (region, size, teaching status) factors. Anaemia was present in 38.7% of patients at admission. Patients with anaemia had a higher 30-day mortality (13.7% vs. 6.3%; p <0.001) and a longer length of stay (geometric mean, 6.9 vs. 6.6 days; p <0.001) compared to patients without anaemia. In multivariable analyses, anaemia remained associated with an increased odds of death (OR 1.82, 95% CI: 1.60-2.06) and a decreased odds of discharge (OR 0.85, 95% CI: 0.82-0.89). Anaemia is very common in patients presenting with PE and is independently associated with an increased short-term mortality and length of stay.

Hierarchical modeling gave plausible estimates of associations between metabolic syndrome and components of antiretroviral therapy

OBJECTIVE: Hierarchical modeling has been proposed as a solution to the multiple exposure problem. We estimate associations between metabolic syndrome and different components of antiretroviral therapy using both conventional and hierarchical models. STUDY DESIGN AND SETTING: We use discrete time survival analysis to estimate the association between metabolic syndrome and cumulative exposure to 16 antiretrovirals from four drug classes. We fit a hierarchical model where the drug class provides a prior model of the association between metabolic syndrome and exposure to each antiretroviral. RESULTS: One thousand two hundred and eighteen patients were followed for a median of 27 months, with 242 cases of metabolic syndrome (20%) at a rate of 7.5 cases per 100 patient years. Metabolic syndrome was more likely to develop in patients exposed to stavudine, but was less likely to develop in those exposed to atazanavir. The estimate for exposure to atazanavir increased from hazard ratio of 0.06 per 6 months' use in the conventional model to 0.37 in the hierarchical model (or from 0.57 to 0.81 when using spline-based covariate adjustment). CONCLUSION: These results are consistent with trials that show the disadvantage of stavudine and advantage of atazanavir relative to other drugs in their respective classes. The hierarchical model gave more plausible results than the equivalent conventional model.

Setting Inventory Levels of CONWIP Flow Lines via Linear Programming

This paper treats the problem of setting the inventory level and optimizing the buffer allocation of closed-loop flow lines operating under the constant-work-in-process (CONWIP) protocol. We solve a very large but simple linear program that models an entire simulation run of a closed-loop flow line in discrete time to determine a production rate estimate of the system. This approach introduced in Helber, Schimmelpfeng, Stolletz, and Lagershausen (2011) for open flow lines with limited buffer capacities is extended to closed-loop CONWIP flow lines. Via this method, both the CONWIP level and the buffer allocation can be optimized simultaneously. The first part of a numerical study deals with the accuracy of the method. In the second part, we focus on the relationship between the CONWIP inventory level and the short-term profit. The accuracy of the method turns out to be best for such configurations that maximize production rate and/or short-term profit.

Impact of anti-inflammatory treatment on the onset of uveitis in juvenile idiopathic arthritis: Longitudinal analysis from a nation-wide paediatric rheumatological database

PURPOSE Based on a nation-wide database, this study analysed the influence of methotrexate (MTX), TNF inhibitors and a combination of the two on uveitis occurrence in JIA patients. METHODS Data from the National Paediatric Rheumatological Database in Germany were used in this study. Between 2002 and 2013, data from JIA patients were annually documented at the participating paediatric rheumatological sites. Patients with JIA disease duration of less than 12 months at initial documentation and ≥2 years of follow-up were included in this study. The impact of anti-inflammatory treatment on the occurrence of uveitis was evaluated by discrete-time survival analysis. RESULTS A total of 3,512 JIA patients (mean age 8.3±4.8 years, female 65.7%, ANA-positive 53.2%, mean age at arthritis onset 7.8±4.8 years) fulfilled the inclusion criteria. Mean total follow-up time was 3.6±2.4 years. Uveitis developed in a total of 180 patients (5.1%) within one year after arthritis onset. Uveitis onset after the first year was observed in another 251 patients (7.1%). DMARD treatment in the year before uveitis onset significantly reduced the risk for uveitis: MTX (HR 0.63, p=0.022), TNF inhibitors (HR 0.56, p<0.001) and a combination of the two (HR 0.10, p<0.001). Patients treated with MTX within the first year of JIA had an even a lower uveitis risk (HR 0.29, p<0.001). CONCLUSION The use of DMARDs in JIA patients significantly reduced the risk for uveitis onset. Early MTX use within the first year of disease and the combination of MTX with a TNF inhibitor had the highest protective effect. This article is protected by copyright. All rights reserved.

Vegetation Changes and Timberline Fluctuations in the Central Alps as Indicators of Holocene Climatic Oscillations

Pollen and plant-macrofossil data are presented for two lakes near the timberline in the Italian (Lago Basso, 2250 m) and Swiss Central Alps (Gouille Rion, 2343 m). The reforestation at both sites started at 9700-9500 BP with Pinus cembra, Larbc decidua, and Betula. The timberline reached its highest elevation between 8700 and 5000 BP and retreated after 5000 BP, due to a mid-Holocene climatic change and increasing human impact since about 3500 BP (Bronze Age). The expansion of Picea abies at Lago Basso between ca. 7500 and 6200 BP was probably favored by cold phases accompanied by increased oceanicity, whereas in the area of Gouille Rion, where spruce expanded rather late (between 4500 and 3500 BP), human influence equally might have been important. The mass expansion of Alnus viridis between ca. 5000 and 3500 BP probably can be related to both climatic change and human activity at timberline. During the early and middle Holocene a series of timberline fluctuations is recorded as declines in pollen and macrofossil concentrations of the major tree species, and as increases in nonarboreal pollen in the pollen percentage diagram of Gouille Rion. Most of ·the periods of low timberline can be correlated by radiocarbon dating with climatic changes in the Alps as indicated by glacier ad­ vances in combination with palynological records, solifluction, and dendrocli­ matical data. Lago Basso and Gouille Rion are the only sites in the Alps showing complete palaeobotanical records of cold phases between 10,000 and 2000 BP with very good time control. The altitudinal range of the Holocene treeline fluc­ tuations caused by climate most likely was not more than 100 to 150 m. A possible correlation of a cold period at ca. 7500-6500 BP (Misox oscil­ lation) in the Alps is made with paleoecological data from North America and Scandinavia and a climatic signal in the GRIP ice core from central Greenland 8200 yr ago (ca. 7400 yr uncal. BP).

Estimating parameters in Markov models for longitudinal studies with missing data or surrogate outcomes

The discrete-time Markov chain is commonly used in describing changes of health states for chronic diseases in a longitudinal study. Statistical inferences on comparing treatment effects or on finding determinants of disease progression usually require estimation of transition probabilities. In many situations when the outcome data have some missing observations or the variable of interest (called a latent variable) can not be measured directly, the estimation of transition probabilities becomes more complicated. In the latter case, a surrogate variable that is easier to access and can gauge the characteristics of the latent one is usually used for data analysis. ^ This dissertation research proposes methods to analyze longitudinal data (1) that have categorical outcome with missing observations or (2) that use complete or incomplete surrogate observations to analyze the categorical latent outcome. For (1), different missing mechanisms were considered for empirical studies using methods that include EM algorithm, Monte Carlo EM and a procedure that is not a data augmentation method. For (2), the hidden Markov model with the forward-backward procedure was applied for parameter estimation. This method was also extended to cover the computation of standard errors. The proposed methods were demonstrated by the Schizophrenia example. The relevance of public health, the strength and limitations, and possible future research were also discussed. ^

Distribution of quality adjusted life expectancy: A systems approach

Statistical methods are developed which assess survival data for two attributes; (1) prolongation of life, (2) quality of life. Health state transition probabilities correspond to prolongation of life and are modeled as a discrete-time semi-Markov process. Imbedded within the sojourn time of a particular health state are the quality of life transitions. They reflect events which differentiate perceptions of pain and suffering over a fixed time period. Quality of life transition probabilities are derived from the assumptions of a simple Markov process. These probabilities depend on the health state currently occupied and the next health state to which a transition is made. Utilizing the two forms of attributes the model has the capability to estimate the distribution of expected quality adjusted life years (in addition to the distribution of expected survival times). The expected quality of life can also be estimated within the health state sojourn time making more flexible the assessment of utility preferences. The methods are demonstrated on a subset of follow-up data from the Beta Blocker Heart Attack Trial (BHAT). This model contains the structure necessary to make inferences when assessing a general survival problem with a two dimensional outcome. ^

An evaluation of sleep hypnotic and stimulant effect on human performance using a computerized psychological test battery

This study evaluated the administration-time-dependent effects of a stimulant (Dexedrine 5-mg), a sleep-inducer (Halcion 0.25-mg) and placebo (control) on human performance. The investigation was conducted on 12 diurnally active (0700-2300) male adults (23-38 yrs) using a double-blind, randomized sixway-crossover three-treatment, two-timepoint (0830 vs 2030) design. Performance tests were conducted hourly during sleepless 13-hour studies using a computer generated, controlled and scored multi-task cognitive performance assessment battery (PAB) developed at the Walter Reed Army Institute of Research. Specific tests were Simple and Choice Reaction Time, Serial Addition/Subtraction, Spatial Orientation, Logical Reasoning, Time Estimation, Response Timing and the Stanford Sleepiness Scale. The major index of performance was "Throughput", a combined measure of speed and accuracy.^ For the Placebo condition, Single and Group Cosinor Analysis documented circadian rhythms in cognitive performance for the majority of tests, both for individuals and for the group. Performance was best around 1830-2030 and most variable around 0530-0700 when sleepiness was greatest (0300).^ Morning Dexedrine dosing marginally enhanced performance an average of 3% with reference to the corresponding in time control level. Dexedrine AM also increased alertness by 10% over the AM control. Dexedrine PM failed to improve performance with reference to the corresponding PM control baseline. With regard to AM and PM Dexedrine administrations, AM performance was 6% better with subjects 25% more alert.^ Morning Halcion administration caused a 7% performance decrement and 16% increase in sleepiness and a 13% decrement and 10% increase in sleepiness when administered in the evening compared to corresponding in time control data. Performance was 9% worse and sleepiness 24% greater after evening versus morning Halcion administration.^ These results suggest that for evening Halcion dosing, the overnight sleep deprivation occurring in coincidence with the nadir in performance due to circadian rhythmicity together with the CNS depressant effects combine to produce performance degradation. For Dexedrine, morning administration resulted in only marginal performance enhancement; Dexedrine in the evening was less effective, suggesting the 5-mg dose level may be too low to counteract the partial sleep deprivation and nocturnal nadir in performance. ^

(Table 1) 40Ar-39Ar incremental heating ages for ODP Hole 163-988A basalt and plagioclase

Results of 40Ar-39Ar Ar dating constrain the age of the submerged volcanic succession, part of the seaward-dipping reflector sequence of the Southeast Greenland volcanic rifted margin, recovered during Leg 163. At the 63ºN drilling transect, the fully normally magnetized volcanic units at Holes 989B (Unit 1) and 990A (Units 1 and 2) are dated at 57.1 ± 1.3 Ma and 55.6 ± 0.6 Ma, respectively. This correlates with a common magnetochron, C25n. The underlying, reversely magnetized lavas at Hole 990A (Units 3-13) yield an average age of 55.8 ± 0.7 Ma and may correlate with C25r. The argon data, however, are also consistent with eruption of the lavas at Site 990 during the very earliest portion of C24. If so, the normally polarized units have to be correlated to a cryptochron (e.g., C24r-11 at ~55.57 Ma). The lavas at Holes 989B and 990A have typical oceanic compositions, implying that final plate separation between Greenland and northwest Europe took place at ~56 Ma. The age for Hole 989B lava is younger than expected from the seismic interpretations, posing questions about the structural evolution of the margin. An age of 49.6 ± 0.2 Ma for the basaltic lava at Site 988 (~66ºN) points to the importance of postbreakup tholeiitic magmatism at the rifted margin. Together with results from Leg 152, a virtually complete time frame for ~12 m.y. of pre-, syn-, and postbreakup volcanism during rifted margin evolution in Southeast Greenland can now be assembled. This time frame includes continental type volcanism at ~61-60 Ma, synbreakup volcanism beginning at ~57 Ma, and postbreakup volcanism at ~49.6 Ma. These discrete time windows coincide with distinct periods of tholeiitic magmatism from the onshore East Greenland Tertiary Igneous Province and is consistent with discrete mantle-melting events triggered by plume arrival (~61-60 Ma) under central Greenland, continental breakup (~57-54 Ma), and passage of the plume axis beneath the East Greenland rifted margin after breakup (~50-49 Ma), respectively.

Efecto de tagetes spp. sobre dos áfidos plagas de Lactuta Sativa (L)

Se evaluó la eficacia de Tagetes spp. como cultivo intercalar y extracto natural sobre la fluctuación poblacional de áfidos en el cultivo de Lactuca sativa (L.). Se realizó un diseño en bloques completamente aleatorizado, siendo la planta la unidad de muestreo. Se consideraron tres tratamientos: testigo (T), cultivo intercalado con Tagetes sp. (CI) y cultivo pulverizado con extracto natural de Tagetes sp. (CP) (n=6). Los datos obtenidos se sometieron a un ANOVA y test de Tukey, según los lineamientos de ensayos repetidos en el tiempo. La densidad poblacional de áfidos fue mayor en el testigo y menor en el cultivo pulverizado, comprobándose una densidad media en el cultivo intercalar.

Siliceous fossils in sediments of the Ibero-Moroccan shelf and adjacent deep sea plains

Siliceous skeletons were investigated in two core profiles (9 cores), one off Cap de Sines, Portugal and the other off Cap de Mazagan, Morocco. Total number of skeletons was determined per gram of dried sediment at different core depths of the fraction >21 µ. Results are compared with a core profile from the Arabian Sea. Diatoms are of four groups: (A) marine-planktonic, B) marine-benthic, (C) freshwater and (D) Tertiary species (Trinacria e.g.). Species from groups (B), (C) and (D) are redeposited in all cores taken at a water depth of greater than 100 m. Small numbers of Silicoflagellates and Radiolarians were found throughout the cores from the Ibero-Moroccan shelf. In the Arabian Sea core, Radiolarians were concentrated in distinct horizons in which Tertiary material was redeposited (40-50, 140-150, 250-260 cm). The number of siliceous skeletons per gram of dried sediment decreases more or less rapidly with increasing depth in all cores. Whereas about 2500 skeletons were found in sediments close to the surface, approximately 100 skeletons only were found in deeper (>40 cm) layers. Deeper horizons with more than 100 specimens were interpreted as redeposited material. This sediment contained robust skeletons, resistant against dissolution, as well as benthic and Tertiary material. The decrease of siliceous skeletons relative to core depth depends upon the sedimentation rate. Where the sedimentation rate is high, the opal dissolution zone extends down to 30-60 cm, where the sedimentation rate is low, it is located at 10-30 cm. Below these depths opals disappears. These zones also have approximately the same age (4000 years) everywhere. Siliceous skeletons dissolve differentially, first the Silicoflagellates disappear, second the Diatoms, third the Radiolarians, and fourth the Sponge Spicules. Surface structure of skeletons from near the opal dissolution zones are similar to those of skeletons treated with NaOH. Tertiary diatoms (Trinacria e. g.) and benthic diatoms (Campylodiscus e.g.) dissolve less rapidly than skeletons of modern planktonic diatoms (Coscinodiscus e.g.). The time control of the opal dissolution zones appeared rather independent of various oceanic influences. No evidence was found for effects from upwelling either off Portugal or off Morocco. No difference in dissolution rates was recorded between the abyssal plains lying off these two areas. Likewise, there was no change in solution rates from Pleistocene to Holocene within either one of the abyssal plains. The Mediterranean outflow, which is enriched in dissolved silica, apparently had no effect on dissolution rates of siliceous skeletons in the sediment.

Stable isotope record of sediment core MD98-2177

We present a reconstruction of El Niño Southern Oscillation (ENSO) variability spanning the Medieval Climate Anomaly (MCA, A.D. 800-1300) and the Little Ice Age (LIA, A.D. 1500-1850). Changes in ENSO are estimated by comparing the spread and symmetry of d18O values of individual specimens of the thermocline-dwelling planktonic foraminifer Pulleniatina obliquiloculata extracted from discrete time horizons of a sediment core collected in the Sulawesi Sea, at the edge of the western tropical Pacific warm pool. The spread of individual d18O values is interpreted to be a measure of the strength of both phases of ENSO while the symmetry of the d18O distributions is used to evaluate the relative strength/frequency of El Niño and La Niña events. In contrast to previous studies, we use robust and resistant statistics to quantify the spread and symmetry of the d18O distributions; an approach motivated by the relatively small sample size and the presence of outliers. Furthermore, we use a pseudo-proxy approach to investigate the effects of the different paleo-environmental factors on the statistics of the d18O distributions, which could bias the paleo-ENSO reconstruction. We find no systematic difference in the magnitude/strength of ENSO during the Northern Hemisphere MCA or LIA. However, our results suggest that ENSO during the MCA was skewed toward stronger/more frequent La Niña than El Niño, an observation consistent with the medieval megadroughts documented from sites in western North America.