Search

Wir wollen uns in diesem Kapitel damit beschaftigen, wie die Wahrscheinlichkeitstheorie und die stochastische Analysis in der Finanzmathematik angewendet werden. Das wesentliche Ergebnis wird die beruhmte Black-Scholes-Bewertungsformel zur Ermittlung des fairen (risikoneutralen) Preises einer Finanzoption sein, welche auf Black, Scholes und Merton zuruckgeht.

Die moderne Finanzmathematik hat sich insbesondere durch die Finanzkrise 2007/2008 stark verandert. Die Finanzkrise hat verdeutlicht, dass klassische Finanzmodelle gerade in extremen Marktsituationen die Realitat nicht immer adaquat abbilden bzw. teilweise auch gar nicht mehr funktionieren. Hierauf sind wir bereits vereinzelt in den vorherigen Abschnitten eingegangen. In diesem Kapitel wollen wir einen Uberblick zu den aktuell wichtigen finanzmathematischen Fragestellungen geben und hierbei nicht nur auf die Finanzkrise, sondern auch auf die Ablosung bzw. Reform der Interbanken-Zinssatze (IBORs) eingehen.

Bevor wir uns mit der Finanzmathematik beschaftigen konnen, ist es notwendig, in diesem ersten Kapitel einige Grundlagen zur Wahrscheinlichkeitstheorie und stochastischen Analysis zu erarbeiten. Hierbei werden wir diverse Lemmata und Satze auffuhren, ohne diese zu beweisen, da wir an der Anwendung und nicht an der detaillierten Herleitung der Grundlagen interessiert sind. Fur die Anwendung ist es jedoch wichtig, Definitionen zu verstehen und relevante Satze (z. B. die Ito-Formel) zu kennen.

In den vorherigen Abschnitten haben wir gezeigt, dass der Preis einer Option von den Parametern \(S_0,K,T,r\) und \(\sigma \) abhangt. Im Weiteren bezeichnen wir daher mit \(V(S_0,K,T,r,\sigma )\) den Modellpreis einer Option basierend auf den Inputparametern und wollen uns nun mit der Frage beschaftigen, wie die Parameter ermittelt werden konnen. Der Aktienpreis \(S_0\) kann zum heutigen Zeitpunkt einfach am Markt abgelesen werden. Die Laufzeit T und der Strike K sind vertraglich festgelegt. Die Parameter r und \(\sigma \) konnen entweder aus Marktpreisen abgeleitet oder historisch geschatzt werden (Letzteres ist weniger relevant und kommt im Allgemeinen auch nur fur Volatilitaten in Frage; siehe Abschn. 2.1.2). Das Ableiten von Bewertungsparametern aus Marktpreisen nennt man auch Bootstrapping oder Kalibrierung des Modells. Wir werden die Methoden hierzu im Weiteren vorstellen. Daruber hinaus wollen wir in diesem Kapitel verallgemeinerte Modelle zur adaquaten Modellierung von Volatilitaten und Zinsen analysieren.

Background/Aims: There is increasing evidence that exposure to air pollutants, including particulate matter (PM2.5, PM10), nitrogen dioxide (NO2), and sulfur dioxide (SO2), might aggravate preexisting skin diseases such as eczema and urticaria. Here we investigated if a possible link exists between air pollution and acne vulgaris. We assessed the association between ambient air pollutant concentrations and the number of visits of patients for acne vulgaris to a dermatological outpatient clinic in Beijing, China, from April 1, 2012 to April 30, 2014. Methods: In this time period, 59,325 outpatient visits were recorded because of acne vulgaris. Daily air pollution parameters for PM10, PM2.5, SO2, and NO2 were obtained from the Beijing Municipal Environmental Monitoring Center. Results: Increased concentrations of ambient PM2.5, PM10, and NO2 were significantly associated with increased numbers of outpatient visits for acne vulgaris over the 2 years. These effects could be observed for NO2 in a single-pollutant model and for PM2.5, PM10, and NO2 in 2-pollutant models, which are closer to real-life exposure. Of note, these effects were specific because they were not observed for increased SO2 concentrations, which even showed negative correlations in all test models. Conclusion: This study provides indirect evidence for a link between acne vulgaris and air pollution.

In this paper we study the optimal dividend problem where the surplus process of an insurance company is modeled by a Cramer–Lundberg model. As distinguished from classical models, we assume that the insurer can continue doing business although the surplus becomes negative, but penalty payments occur, depending on the level of the surplus. The higher the surplus level, the lower the penalty payments. The penalty payments are rather technical and necessary to avoid that losses can rise above any number. Nevertheless, the concept can also be reasonable in practice. For example, penalty payments can occur if the insurer needs to borrow money. The aim is to determine a dividend strategy that maximizes the difference between the expected discounted dividend and penalty payments. We show that the optimal strategy is a barrier strategy. As examples, exponential and linear penalty payments are considered.

We study the optimal dividend problem where the surplus process of an insurance company is modelled by a diffusion process. The insurer is not ruined when the surplus becomes negative, but penalty payments occur, depending on the level of the surplus. The penalty payments shall avoid that losses can rise above any number and can be seen as a preference measure or costs for negative capital. As examples, exponential and linear penalty payments are considered. It turns out that a barrier dividend strategy is optimal.

During the last two decades, it has been well established that a short-term exposure to ozone (O3) elicits an oxidative stress response in human and mouse skin, which leads to aberrant transcriptional expression of genes consistent with increased skin aging. Whether a long-term exposure to ambient O3 is associated with any skin aging traits, has remained unclear. We addressed this question in two elderly German cohorts: the SALIA study (806 women aged 66–79 years), and the BASE-II study (1207 men and women aged 60–84 years). Five-year mean residential exposure to O3 was modeled as the number of days with maximum daily 8-h mean O3 concentrations ≥120 μg/m3 per year in the wider neighborhood (5-digit postcode) of a participant's residence. Extrinsic (environmentally induced) skin aging traits – coarse wrinkles and pigment spots (lentigines) on the face – were assessed by means of SCINEXA™, a validated visual score previously shown to be well suited to measure extrinsic facial skin aging in cohort studies. We observed positive associations of O3 exceedances with coarse wrinkles in the face, but not with pigment spots. These associations were present in each cohort as well as in the combined sample of both cohorts. They were independent of chronic ultraviolet radiation exposure as the most obvious confounder, and also of co-pollutants such as particulate matter and nitrogen dioxide. Thus, long-term exposure to elevated concentrations of tropospheric O3 appears to contribute to skin aging. Keywords: Tropospheric ozone, Air pollution, Skin aging, Skin wrinkling

Mammalian sirtuins are involved in the control of metabolism and life-span regulation. Here, we link the mitochondrial sirtuin SIRT4 with cellular senescence, skin aging, and mitochondrial dysfunction. SIRT4 expression significantly increased in human dermal fibroblasts undergoing replicative or stress-induced senescence triggered by UVB or gamma-irradiation. In-vivo, SIRT4 mRNA levels were upregulated in photoaged vs. non-photoaged human skin. Interestingly, in all models of cellular senescence and in photoaged skin, upregulation of SIRT4 expression was associated with decreased levels of miR-15b. The latter was causally linked to increased SIRT4 expression because miR-15b targets a functional binding site in the SIRT4 gene and transfection of oligonucleotides mimicking miR-15b function prevented SIRT4 upregulation in senescent cells. Importantly, increased SIRT4 negatively impacted on mitochondrial functions and contributed to the development of a senescent phenotype. Accordingly, we observed that inhibition of miR-15b, in a SIRT4-dependent manner, increased generation of mitochondrial reactive oxygen species, decreased mitochondrial membrane potential, and modulated mRNA levels of nuclear encoded mitochondrial genes and components of the senescence-associated secretory phenotype (SASP). Thus, miR-15b is a negative regulator of stress-induced SIRT4 expression thereby counteracting senescence associated mitochondrial dysfunction and regulating the SASP and possibly organ aging, such as photoaging of human skin.

Genetic and environmental risk factors contribute to the pathogenesis of Alzheimer’s dementia. Besides known genetic risk factors like the apolipoprotein (APO) Ee4 allele, single nuclear polymorphisms (SNPs) of the estrogen receptors (ESRs) are candidate genetic risk factors, while air pollution represents an environmental risk factor for dementia. Effects of these risk factors and their interaction were investigated in the SALIA cohort of 834 non-demented elderly women. Cognitive function was assessed by the CERAD-plus test battery. Air pollution was estimated by land use regression (LUR) models. Genotyping was carried out for nine ESR1 and ESR2 SNPs and two ApoE SNPs. Carriers of minor ESR2 alleles showed significantly reduced cognitive performance in the CERAD total score with most pronounced deficits in semantic memory (rs1256062, rs10144225, and rs2274705) and executive function (rs1256062). The minor allele effects of ESR2 were stronger in carriers of APOEe4 for the cognitive domain ‘executive function’ (p value of interaction 0.023 for rs1256062). The investigated ESR1 SNPs were not associated with cognition. Furthermore, we found a significant gene–environment interaction between the ESR2 SNP rs1256062 and air pollution on cognition. Carriers of two major alleles of rs1256062 were more susceptible for an air pollution-induced decrease in performance of ‘figure copying’ than carriers of minor alleles (p value of interaction, e.g., 0.031 for PM2.5). In conclusion, ESR2 but not ESR1 minor alleles were associated with lower cognitive performance in elderly women with an indication of a gene–gene interaction with APOEe4. We also found indications for gene–environment interactions of ESR2 with traffic-related air pollution exposure on cognitive performance.

Few studies have evaluated the prevalence of skin tumours in the geriatric population and none have analysed different skin aging parameters for whole-body skin in this population. To evaluate the prevalence of skin tumours and global skin aging in a French cohort of elderly people. In total, 209 subjects, 105 women and 104 men (mean age: 77.5; range: 74-81 years), were enrolled from the PROOF (PROgnostic indicator OF cardiovascular and cerebrovascular events) cohort. SCINEXA (SCore for INtrinsic and EXtrinsic skin Aging) was used to assess the degree of skin aging and the prevalence of skin tumours. Some additional cutaneous parameters were also studied. Skin aging in women and men was compared. Mean global SCINEXA was 24.3 (SD: 4.7; range: 8.2-35.3). Solar elastosis and lax appearance were more severe in women (t test; p

This paper considers an optimal investment and reinsurance problem for an insurance company, where the surplus follows a linear diffusion. Contrary to classical models the insurer can continue doing business even if the surplus becomes negative, but penalty payments occur depending on the level of the current surplus. The insurer can invest in n risky assets and reduce the insurance risk either by excess of loss or by proportional reinsurance. The aim is to find an optimal investment and reinsurance strategy which minimises the penalty payments. We consider various penalty functions and derive closed form solutions.

Schaut man in einem dermatologischen Lehrbuch nach, so wird der Begriff extrinsische Hautalterung in der Regel synonym verwendet mit „Lichtalterung“ der Haut. Unbestreitbar ist, dass eine chronische Bestrahlung mit ultraviolettem Licht, insbesondere als Bestandteil des naturlichen Sonnenlichtes, einen, wenn nicht den wesentlichen Grund fur umweltinduzierte Hautalterungsprozesse darstellt. In den letzten Jahren ist aber sehr deutlich geworden, dass weitere Umweltfaktoren am vorzeitigen Alterungsprozess der Haut kausal beteiligt sind.

Background As life expectancy is increasing and healthy ageing becomes more and more important, skin ageing is a growing topic of interest from both a medical and a commercial point of view. The urgency to unravel the causes of skin ageing is rising. However, there is a lack of objective, simple, noninvasive methods to assess biological skin age - a term introduced to describe how old someone looks, covering both the appearance and function of the skin. A rapid, noninvasive assessment of biological skin age would greatly facilitate the execution of the studies required to find the causes of skin ageing.Objectives To find an objective, easy-to-apply method to assess biological skin age.Methods Skin age score (SAS) was compared with skin autofluorescence, a measure of advanced glycation end products in the skin, and several subject characteristics in 32 healthy, white women with little sun-exposed skin and no history of smoking.Results A moderate, positive correlation (R-2 = 0.32, P = 0.001) between SAS and skin autofluorescence-based biological skin age was found. However, the variation in biological skin age according to SAS could be explained better by body mass index, chronological age and hormonal status (R-2 = 0.86, P Conclusions In the current setting skin autofluorescence did not contribute better to the prediction of biological skin age than chronological age. Biological skin age was best predicted by body mass index, chronological age and hormonal status, and this approach provides a considerable simplification of the application of biological skin age.