Mathematical Aspects of Financial Markets with Frictions

Frictions are factors that hinder trading of securities in financial markets. Typical frictions include limited market depth, transaction costs, lack of infinite divisibility of securities, and taxes. Conventional models used in mathematical finance often gloss over these issues, which affect almost all financial markets, by arguing that the impact of frictions is negligible and, consequently, the frictionless models are valid approximations. This dissertation consists of three research papers, which are related to the study of the validity of such approximations in two distinct modeling problems. Models of price dynamics that are based on diffusion processes, i.e., continuous strong Markov processes, are widely used in the frictionless scenario. The first paper establishes that diffusion models can indeed be understood as approximations of price dynamics in markets with frictions. This is achieved by introducing an agent-based model of a financial market where finitely many agents trade a financial security, the price of which evolves according to price impacts generated by trades. It is shown that, if the number of agents is large, then under certain assumptions the price process of security, which is a pure-jump process, can be approximated by a one-dimensional diffusion process. In a slightly extended model, in which agents may exhibit herd behavior, the approximating diffusion model turns out to be a stochastic volatility model. Finally, it is shown that when agents' tendency to herd is strong, logarithmic returns in the approximating stochastic volatility model are heavy-tailed. The remaining papers are related to no-arbitrage criteria and superhedging in continuous-time option pricing models under small-transaction-cost asymptotics. Guasoni, Rásonyi, and Schachermayer have recently shown that, in such a setting, any financial security admits no arbitrage opportunities and there exist no feasible superhedging strategies for European call and put options written on it, as long as its price process is continuous and has the so-called conditional full support (CFS) property. Motivated by this result, CFS is established for certain stochastic integrals and a subclass of Brownian semistationary processes in the two papers. As a consequence, a wide range of possibly non-Markovian local and stochastic volatility models have the CFS property.

Molecular and epidemiological aspects of Streptococcus pyogenes disease in Finland: Severe infections and bacterial, non-necrotizing cellulitis

Streptococcus pyogenes (group A streptococcus) is an important human pathogen, causing a wide array of infections ranging in severity. The majority of S. pyogenes infections are mild upper respiratory tract or skin infections. Severe, invasive infections, such as bacteraemia, are relatively rare, but constitute a major global burden with a high mortality. Certain streptococcal types are associated with a more severe disease and higher mortality. Bacterial, non-necrotizing cellulitis and erysipelas are localised infections of the skin, and although they are usually not life-threatening, they have a tendency to recur and therefore cause substantial morbidity. Despite several efforts aimed at developing an effective and safe vaccine against S. pyogenes infections, no vaccine is yet available. In this study, the epidemiology of invasive S. pyogenes infections in Finland was described over a decade of national, population-based surveillance. Recent trends in incidence, outcome and bacterial types were investigated. The beta-haemolytic streptococci causing cellulitis and erysipelas infections in Finland were studied in a case-control study. Bacterial isolates were characterised using both conventional and molecular typing methods, such as the emm typing, which is the most widely used typing method for beta-haemolytic streptococci. The incidence of invasive S. pyogenes disease has had an increasing trend during the past ten years in Finland, especially from 2006 onwards. Age- and sex-specific differences in the incidence rate were identified, with men having a higher incidence than women, especially among persons aged 45-64 years. In contrast, more infections occurred in women aged 25-34 years than men. Seasonal patterns with occasional peaks during the midsummer and midwinter were observed. Differences in the predisposing factors and underlying conditions of patients may contribute to these distinctions. Case fatality associated with invasive S. pyogenes infections peaked in 2005 (12%) but remained at a reasonably low level (8% overall during 2004-2007) compared to that of other developed countries (mostly exceeding 10%). Changes in the prevalent emm types were associated with the observed increases in incidence and case fatality. In the case-control study, acute bacterial non-necrotizing cellulitis was caused predominantly by Streptococcus dysgalactiae subsp. equisimilis, instead of S. pyogenes. The recurrent nature of cellulitis became evident. This study adds to our understanding of S. pyogenes infections in Finland and provides a basis for comparison to other countries and future trends. emm type surveillance and outcome analyses remain important for detecting such changes in type distribution that might lead to increases in incidence and case fatality. Bacterial characterisation serves as a basis for disease pathogenesis studies and vaccine development.

New aspects of the diagnosis of Helicobacter pylori infection

Aims: Helicobacter pylori infection, although the prevalence is declining in Western world, is still responsible for several clinically important diseases. None of the diagnostic tests is perfect and in this study, the performance of three stool antigen tests was assessed. In areas of high H. pylori prevalence, the definition of patients with the greatest benefit from eradication therapy may be a problem; the role of duodenal gastric metaplasia in categorizing patients at risk for duodenal ulcer was evaluated in this respect. Whether persistent chronic inflammation and elevated H. pylori antibodies after successful eradication are associated with each other or with atrophic gastritis, a long term sequelae of H. pylori infection, were also studied. Patients and methods: The three stool antigen tests were assessed in pre- and post-eradication settings among 364 subjects in two studies as compared to the rapid urease test (RUT), histology, culture, the 13C-urea breath test (UBT) and enzyme immunoassay (EIA) based H. pylori serology. The association between duodenal gastric metaplasia with duodenal ulcer was evaluated in a retrospective study including 1054 patients gastroscopied due to clinical indications and 154 patients previously operated for duodenal ulcer. The extent of duodenal gastric metaplasia was assessed from histological specimens in different patient groups formed on the basis of gastroscopy findings and H. pylori infection. Chronic gastric inflammation (108 patients) and H. pylori antibodies and serum markers for atrophy (77 patients) were assessed in patients earlier treated for H. pylori. Results: Of the stool antigen tests studied, the monoclonal antibody-based EIA-test showed the highest sensitivity and specificity both in the pre-treatment setting (96.9% and 95.9%) and after therapy (96.9% and 97.8%). The polyclonal stool antigen test and the in-office test had at baseline a sensitivity of 91% and 94%, and a specificity of 96% and 89%, respectively and in a post-treatment setting, a sensitivity of 78% and 91%, and a specificity of 97%, respectively. Duodenal gastric metaplasia was strongly associated with H. pylori positive duodenal ulcer (odds ratio 42). Although common still five years after eradication, persistent chronic gastric inflammation (21%) and elevated H. pylori antibodies (33%) were neither associated with each other nor with atrophic gastritis. Conclusions: Current H. pylori infection can feasibly be diagnosed by a monoclonal antibody-based EIA test with the accuracy comparable to that of reference methods. The performance of the polyclonal test as compared to the monoclonal test was inferior especially in the post-treatment setting. The in-office test had a low specificity for primary diagnosis and hence positive test results should probably be confirmed with another test before eradication therapy is prescribed. The presence of widespread duodenal gastric metaplasia showed promising results in detecting patients who should be treated for H. pylori due to an increased risk of duodenal ulcer. If serology is used later on in patients with earlier successfully treated for H. pylori, it should be taken into account that H. pylori antibodies may persist elevated for years for unknown reason. However, this phenomenon was not found to be associated with persistent chronic inflammation or atrophic changes.

Bioavailability aspects of hydrophobic contaminant degradation in soils

This thesis concentrates on bioavailability of organic soil contaminants in the context of bioremediation of soil contaminated with volatile or non-volatile hydrophobic pollutants. Bioavailability and biodegradation was studied from four viewpoints: (i) Improvement of bioavailability and biodegradation of volatile hydrocarbons in contained bioremediation systems at laboratory - and pilot-scale. (ii) Improvement of bioavailability of non-volatile, hydrophobic compounds in such systems. (iii) Biodegradation of a non-volatile hydrophobic compound in soil organic matter in microcosms. (iiii) Bioavailability of nitrogen in an open, full-scale bioremediation system. It was demonstrated that volatility of organic compounds can be controlled by amending the soil with adsorbents. The sorbed hydrocarbons were shown to be available to soil microbiota. As the result, biodegradation of the volatile hydrocarbons was greatly favored at the expense of volatilization. PAH compounds were shown to be mobilized and their bioavailability improved by a hydrophobic, non-toxic additive, vegetable oil. Bioavailability of the PAHs was recorded as an increased toxicity of the soil. In spite of the increased bioavailability, biodegradation of the PAHs decreased. In microcosms simulating boreal forest organic surface soil, PAH-compound (pyrene) was shown to be removed from soil biologically. Therefore hydrophobicity of the substrate does not necessarily mean low availability and biodegradation in organic soil. Finally, in this thesis it was demonstrated that an unsuitable source of nitrogen or its overdose resulted in wasteful spending of this nutrient and even harmful effects on soil microbes. Such events may inhibit rather than promote the bioremediation process in soil.

Aspects of atomic decompositions and Bergman projections

The concept of an atomic decomposition was introduced by Coifman and Rochberg (1980) for weighted Bergman spaces on the unit disk. By the Riemann mapping theorem, functions in every simply connected domain in the complex plane have an atomic decomposition. However, a decomposition resulting from a conformal mapping of the unit disk tends to be very implicit and often lacks a clear connection to the geometry of the domain that it has been mapped into. The lattice of points, where the atoms of the decomposition are evaluated, usually follows the geometry of the original domain, but after mapping the domain into another this connection is easily lost and the layout of points becomes seemingly random. In the first article we construct an atomic decomposition directly on a weighted Bergman space on a class of regulated, simply connected domains. The construction uses the geometric properties of the regulated domain, but does not explicitly involve any conformal Riemann map from the unit disk. It is known that the Bergman projection is not bounded on the space L-infinity of bounded measurable functions. Taskinen (2004) introduced the locally convex spaces LV-infinity consisting of measurable and HV-infinity of analytic functions on the unit disk with the latter being a closed subspace of the former. They have the property that the Bergman projection is continuous from LV-infinity onto HV-infinity and, in some sense, the space HV-infinity is the smallest possible substitute to the space H-infinity of analytic functions. In the second article we extend the above result to a smoothly bounded strictly pseudoconvex domain. Here the related reproducing kernels are usually not known explicitly, and thus the proof of continuity of the Bergman projection is based on generalised Forelli-Rudin estimates instead of integral representations. The minimality of the space LV-infinity is shown by using peaking functions first constructed by Bell (1981). Taskinen (2003) showed that on the unit disk the space HV-infinity admits an atomic decomposition. This result is generalised in the third article by constructing an atomic decomposition for the space HV-infinity on a smoothly bounded strictly pseudoconvex domain. In this case every function can be presented as a linear combination of atoms such that the coefficient sequence belongs to a suitable Köthe co-echelon space.

Living Poetically in the Modern Age : The Situational Aspects of Kierkegaard's Thought

How did Søren Kierkegaard (1813 1855) situate the human subject into historical and social actuality? How did he take into consideration his own situatedness? As key for understanding these questions the research takes the ideal of living poetically that Kierkegaard outlined in his dissertation. In The Concept of Irony (1841) Kierkegaard took up this ideal of the Romantic ironists and made it into an ethical-religious ideal. For him the ideal of living poetically came to mean 1) becoming brought up by God, while 2) assuming ethical-religiously one s role and place in the historical actuality. Through an exegesis of Kierkegaard s texts from 1843 to 1851 it is shown how this ideal governed Kierkegaard s thought and action throughout his work. The analysis of Kierkegaard s ideal of living poetically not only a) shows how the Kierkegaardian subject is situated in its historical context. It also b) sheds light on Kierkegaard s social and political thought, c) helps to understand Kierkegaard s character as a religious thinker, and d) pits his ethical-religious orientation in life against its scientific and commonsense alternatives. The research evaluates the rationality of the way of life championed by Kierkegaard by comparing it with ways of life dominated by reflection and reasoning. It uses Kierkegaard s ideal of living poetically in trying to understand the tensions between religious and unreligious ways of life.

Genetic aspects of outcome in kidney transplantation: cytokine and thrombosis associated candidate genes and gene expression biomarkers

Kidney transplantation (Tx) is the treatment of choice for end stage renal disease. Immunosuppressive medications are given to prevent an immunological rejection of the transplant. However, immunosuppressive drugs increase e.g. the risk of infection, cancer or nephrotoxicity. A major genetic contributors to immunological acceptance of the graft are human leukocyte antigen (HLA) genes. Also other non-HLA gene polymorphisms may predict the future risk of complications before Tx, possibly enabling individualised immunotherapy. Graft function after Tx is monitored using non-specific clinical symptoms and laboratory markers. The definitive diagnosis of graft rejection however relies on a biopsy of the graft. In the acute rejection (AR) diagnostics there is a need for an alternative to biopsy that would be an easily repeatable and simple method for regular use. Frequent surveillance of acute or subclinical rejection (SCR) may improve long-term function. In this thesis, associations between cytokine and thrombosis associated candidate genes and the outcome of kidney Tx were studied. Cytotoxic and co-stimulatory T lymphocyte molecule gene expression biomarkers for the diagnosis of the AR and the SCR were also investigated. We found that polymorphisms in the cytokine genes tumor necrosis factor and interleukin 10 (IL10) of the recipients were associated with AR. In addition, certain IL10 gene polymorphisms of the donors were associated with the incidence of cytomegalovirus infection and occurrence of later infection in a subpopulation of recipients. Further, polymorphisms in genes related to the risk of thrombosis and those of certain cytokines were not associated with the occurrence of thrombosis, infarction, AR or graft survival. In the study of biomarkers for AR, whole blood samples were prospectively collected from adult kidney Tx patients. With real-time quantitative PCR (RT-QPCR) gene expression quantities of CD154 and ICOS differentiated the patients with AR from those without, but not from the patients with other causes of graft dysfunction. Biomarkers for SCR were studied in paediatric kidney Tx patients. We used RT-QPCR to quantify the gene expression of immunological candidate genes in a low-density array format. In addition, we used RT-QPCR to validate the results of the microarray analysis. No gene marker differentiated patients with SCR from those without SCR. This research demonstrates the lack of robust markers among polymorphisms or biomarkers in investigated genes that could be included in routine analysis in a clinical laboratory. In genetic studies, kidney Tx can be regarded as a complex trait, i.e. several environmental and genetic factors may determine its outcome. A number of currently unknown genetic factors probably influence the results of Tx.

Clinical aspects of exhaled nitric oxide in adults : Associations with atopy, bronchial hyperresponsiveness, smoking and chronic obstruction

Measurement of fractional exhaled nitric oxide (FENO) has proven useful in assessment of patients with respiratory symptoms, especially in predicting steroid response. The objective of these studies was to clarify issues relevant for the clinical use of FENO. The influence of allergic sensitization per se on FENO in healthy asymptomatic subjects was studied, the association between airway inflammation and bronchial hyperresponsiveness (BHR) in steroid-naive subjects with symptoms suggesting asthma was examined, as well as the possible difference in this association between atopic and nonatopic subjects. Influence of smoking on FENO was compared between atopic and nonatopic steroid-naive asthmatics and healthy subjects. The short-term repeatability of FENO in COPD patients was examined in order to assess whether the degree of chronic obstruction influences the repeatability. For these purposes, we studied a random sample of 248 citizens of Helsinki, 227 army conscripts with current symptoms suggesting asthma, 19 COPD patients, and 39 healthy subjects. FENO measurement, spirometry and bronchodilatation test, structured interview. skin prick tests, and histamine and exercise challenges were performed. Among healthy subjects with no signs of airway diseases, median FENO was similar in skin prick test-positive and –negative subjects, and the upper normal limit of FENO was 30 ppb. In atopic and nonatopic subjects with symptoms suggesting asthma, FENO associated with severity of exercise- or histamine-induced BHR only in atopic patients. FENO in smokers with steroid-naive asthma was significantly higher than in healthy smokers and nonsmokers. Among atopic asthmatics, FENO was significantly lower in smokers than in nonsmokers, whereas no difference appeared among nonatopic asthmatics. The 24-h repeatability of FENO was equally good in COPD patients as in healthy subjects. These findings indicate that allergic sensitization per se does not influence FENO, supporting the view that elevated FENO indicates NO-producing airway inflammation, and that same reference range can be applied to both skin prick test-positive and -negative subjects. The significant correlation between FENO and degree of BHR only in atopic steroid-naive subjects with current asthmatic symptoms supports the view that pathogenesis of BHR in atopic asthma is strongly involved in NO-producing airway inflammation, whereas in development of BHR in nonatopic asthma other mechanisms may dominate. Attenuation of FENO only in atopic but not in nonatopic smokers with steroid-naive asthma may result from differences in mechanisms of FENO formation as well as in sensitivity of these mechanisms to smoking in atopic and nonatopic asthma. The results suggest, however, that in young adult smokers, FENO measurement may prove useful in assessment of airway inflammation. The short-term repeatability of FENO in COPD patients with moderate to very severe disease and in healthy subjects was equally good.

Obstetric and gynaecological aspects of HIV infection

The purpose of the present study was to examine the outcome of pregnancies among HIV-infected women in Helsinki, use of the levonorgestrel-releasing intrauterine system (LNG-IUS) among HIV-infected women and the prevalence and risk factors of cytological and histologically proven cervical lesions in this population. Between 1993 and 2003 a total of 45 HIV-infected women delivered 52 singleton infants. HIV infection was diagnosed during pregnancy in 40% of the mothers. Seventeen of the mothers received antiretroviral (ARV) medication prior to pregnancy and in 34 cases, the medication was started during pregnancy. A good virological response (i.e. HIV RNA load <1000/mL during the last trimester) to ARV medication was achieved in 36/40 (90%) of the patients in whom HI viral load measurements were performed. Of the infants, 92% were born at term, and their mean (±SD) birth weight was 3350±395 g. The Caesarean section rate was low, 25%. All newborns received ARV medication and none of the infants born to mothers with pre-delivery diagnosis of maternal HIV infection were infected. The safety and advantages of the LNG-IUS were studied prospectively (n=12) and retrospectively (n=6). The LNG-IUS was well tolerated and no cases of PID or pregnancy were noted. Menstrual bleeding was reduced significantly during use of the LNG-IUS; this was associated with a slight increase in haemoglobin levels. Serum oestradiol concentrations remained in the follicular range in all subjects. The key finding was that genital shedding of HIV RNA did not change after the insertion of the LNG-IUS. The mean annual prevalence of low-grade squamous intraepithelial lesions (SIL) was 15% and that of high-grade SIL was 5% among 108 systematically followed HIV-infected women during 1989 2003. A reduced CD4 lymphocyte count was associated with an increased prevalence of SIL, whereas duration of HIV infection, use of ARV medication and HI viral load were not. The cumulative risk of any type of SIL was 17% after one year and 48% after five years among patients with initially normal Pap smears. The risk of developing SIL was associated with young age and a high initial HI viral load. During the follow-up 51 subjects (n=153) displayed cervical intraepithelial neoplasia (CIN), (16% CIN1 and 18% CIN 2-3). Only one case of cancer of the uterine cervix was detected. Pap smears were reliable in screening for CIN. Both nulliparity (p<0.01) and bacterial vaginosis (p<0.04) emerged as significant risk factors of CIN. In conclusion, a combination of universal antenatal screening and multidisciplinary management allows individualized treatment and prevents vertical transmission of HIV. Use of the LNG-IUS is safe among HIV-infected women and cervicovaginal shedding of HIV RNA is not affected by use of the LNG-IUS. The risk of cervical pre-malignant lesions is high among HIV-infected women despite systematic follow-up.