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.

Aspects of Arminian Soteriology in Methodist-Lutheran Ecumenical Dialogues in 20th and 21st Century

The aim of this thesis is to analyse the key ecumenical dialogues between Methodists and Lutherans from the perspective of Arminian soteriology and Methodist theology in general. The primary research question is defined as: "To what extent do the dialogues under analysis relate to Arminian soteriology?" By seeking an answer to this question, new knowledge is sought on the current soteriological position of the Methodist-Lutheran dialogues, the contemporary Methodist theology and the commonalities between the Lutheran and Arminian understanding of soteriology. This way the soteriological picture of the Methodist-Lutheran discussions is clarified. The dialogues under analysis were selected on the basis of versatility. Firstly, the sole world organisation level dialogue was chosen: The Church – Community of Grace. Additionally, the document World Methodist Council and the Joint Declaration on the Doctrine of Justification is analysed as a supporting document. Secondly, a document concerning the discussions between two main-line churches in the United States of America was selected: Confessing Our Faith Together. Thirdly, two dialogues between non-main-line Methodist churches and main-line Lutheran national churches in Europe were chosen: Fellowship of Grace from Norway and Kristuksesta osalliset from Finland. The theoretical approach to the research conducted in this thesis is systematic analysis. The Remonstrant articles of Arminian soteriology are utilised as an analysis tool to examine the soteriological positions of the dialogues. New knowledge is sought by analysing the stances of the dialogues concerning the doctrines of partial depravity, conditional election, universal atonement, resistible grace and conditional perseverance of saints. This way information is also provided for approaching the Calvinist-Arminian controversy from new perspectives. The results of this thesis show that the current soteriological position of the Methodist-Lutheran dialogues is closer to Arminianism than Calvinism. The dialogues relate to Arminian soteriology especially concerning the doctrines of universal atonement, resistible grace and conditional perseverance of saints. The commonalities between the Lutheran and Arminian understanding of soteriology exist mainly in these three doctrines as they are uniformly favoured in the dialogues. The most discussed area of soteriology is human depravity, in which the largest diversity of stances occurs as well. On the other hand, divine election is the least discussed topic. The overall perspective, which the results of the analysis provide, indicates that the Lutherans could approach the Calvinist churches together with the Methodists with a wider theological perspective and understanding when the soteriological issues are considered as principal. Human depravity is discovered as the area of soteriology which requires most work in future ecumenical dialogues. However, the detected Lutheran hybrid notion on depravity (a Calvinist-Arminian mixture) appears to provide a useful new perspective for Calvinist-Arminian ecumenism and offers potentially fruitful considerations to future ecumenical dialogues.

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.

Methicillin-resistant Staphylococcus aureus in Finland: recent changes in the epidemiology, long-term facility aspects, and phenotypic and molecular detection of isolates

Staphylococcus aureus is one of the most important bacteria that cause disease in humans, and methicillin-resistant S. aureus (MRSA) has become the most commonly identified antibiotic-resistant pathogen in many parts of the world. MRSA rates have been stable for many years in the Nordic countries and the Netherlands with a low MRSA prevalence in Europe, but in the recent decades, MRSA rates have increased in those low-prevalence countries as well. MRSA has been established as a major hospital pathogen, but has also been found increasingly in long-term facilities (LTF) and in communities of persons with no connections to the health-care setting. In Finland, the annual number of MRSA isolates reported to the National Infectious Disease Register (NIDR) has constantly increased, especially outside the Helsinki metropolitan area. Molecular typing has revealed numerous outbreak strains of MRSA, some of which have previously been associated with community acquisition. In this work, data on MRSA cases notified to the NIDR and on MRSA strain types identified with pulsed-field gel electrophoresis (PFGE), multilocus sequence typing (MLST), and staphylococcal cassette chromosome mec (SCCmec) typing at the National Reference Laboratory (NRL) in Finland from 1997 to 2004 were analyzed. An increasing trend in MRSA incidence in Finland from 1997 to 2004 was shown. In addition, non-multi-drug resistant (NMDR) MRSA isolates, especially those resistant only to methicillin/oxacillin, showed an emerging trend. The predominant MRSA strains changed over time and place, but two internationally spread epidemic strains of MRSA, FIN-16 and FIN-21, were related to the increase detected most recently. Those strains were also one cause of the strikingly increasing invasive MRSA findings. The rise of MRSA strains with SCCmec types IV or V, possible community-acquired MRSA was also detected. With questionnaires, the diagnostic methods used for MRSA identification in Finnish microbiology laboratories and the number of MRSA screening specimens studied were reviewed. Surveys, which focused on the MRSA situation in long-term facilities in 2001 and on the background information of MRSA-positive persons in 2001-2003, were also carried out. The rates of MRSA and screening practices varied widely across geographic regions. Part of the NMDR MRSA strains could remain undetected in some laboratories because of insufficient diagnostic techniques used. The increasing proportion of elderly population carrying MRSA suggests that MRSA is an emerging problem in Finnish long-term facilities. Among the patients, 50% of the specimens were taken on a clinical basis, 43% on a screening basis after exposure to MRSA, 3% on a screening basis because of hospital contact abroad, and 4% for other reasons. In response to an outbreak of MRSA possessing a new genotype that occurred in a health care ward and in an associated nursing home of a small municipality in Northern Finland in autumn 2003, a point-prevalence survey was performed six months later. In the same study, the molecular epidemiology of MRSA and methicillin-sensitive S. aureus (MSSA) strains were also assessed, the results to the national strain collection compared, and the difficulties of MRSA screening with low-level oxacillin-resistant isolates encountered. The original MRSA outbreak in LTF, which consisted of isolates possessing a nationally new PFGE profile (FIN-22) and internationally rare MLST type (ST-27), was confined. Another previously unrecognized MRSA strain was found with additional screening, possibly indicating that current routine MRSA screening methods may be insufficiently sensitive for strains possessing low-level oxacillin resistance. Most of the MSSA strains found were genotypically related to the epidemic MRSA strains, but only a few of them had received the SCCmec element, and all those strains possessed the new SCCmec type V. In the second largest nursing home in Finland, the colonization of S. aureus and MRSA, and the role of screening sites along with broth enrichment culture on the sensitivity to detect S. aureus were studied. Combining the use of enrichment broth and perineal swabbing, in addition to nostrils and skin lesions swabbing, may be an alternative for throat swabs in the nursing home setting, especially when residents are uncooperative. Finally, in order to evaluate adequate phenotypic and genotypic methods needed for reliable laboratory diagnostics of MRSA, oxacillin disk diffusion and MIC tests to the cefoxitin disk diffusion method at both +35°C and +30°C, both with or without an addition of sodium chloride (NaCl) to the Müller Hinton test medium, and in-house PCR to two commercial molecular methods (the GenoType® MRSA test and the EVIGENETM MRSA Detection test) with different bacterial species in addition to S. aureus were compared. The cefoxitin disk diffusion method was superior to that of oxacillin disk diffusion and to the MIC tests in predicting mecA-mediated resistance in S. aureus when incubating at +35°C with or without the addition of NaCl to the test medium. Both the Geno Type® MRSA and EVIGENETM MRSA Detection tests are usable, accurate, cost-effective, and sufficiently fast methods for rapid MRSA confirmation from a pure culture.

Behavioural, population, and genetic processes affecting metapopulation dynamics of the Glanville fritillary butterfly

In my thesis I have been studying the effects of population fragmentation and extinction-recolonization dynamics on genetic and evolutionary processes in the Glanville fritillary butterfly (Melitaea cinxia). By conducting crosses within and among newly-colonized populations and using several fitness measures, I found a strong decrease in fitness following colonization by a few related individuals, and a strong negative relationship between parental relatedness and offspring fitness. Thereafter, I was interested in determining the number and relatedness of individuals colonizing new populations, which I did using a set of microsatellites I had previously developed for this species. Additionally, I am interested in the evolution of key life-history traits. By following the lifetime reproductive success of males emerging at different times in a semi-natural setup, I demonstrated that protandry is adaptive in males, and I was able to rule out, for M. cinxia, alternative incidental hypotheses evoked to explain the evolution of protandry in insects. Finally, in work I did together with Prof. Hanna Kokko, I am proposing bet-hedging as a new mechanism that could explain the evolution of polyandry in M. cinxia.

The life cycle and genetic structure of the red alga Furcellaria lumbricalis on a salinity gradient

The life cycle and genetic diversity of the red alga Furcellaria lumbricalis (Hudson) Lamouroux were investigated in 15 populations in northern Europe. The occurrence of different life cycle phases and seasonality of reproduction were studied in four brackish populations in the northern Baltic Sea. Furthermore, a new method, based on genome screening with ISSR markers combined with a restriction-ligation method, was developed to discover microsatellite markers for population genetic analyses. The mitochondrial DNA cox2-3 spacer sequence and four microsatellite markers were used to examine the genetic diversity and differentiation of red algal populations in northern Europe. In addition, clonality and small-scale genetic structure of one Irish and four Baltic Sea populations were studied with microsatellite markers. It was discovered that at the low salinities of the northern Baltic Sea, only tetrasporophytes and males were present in the populations of F. lumbricalis and that winter was the main season for tetrasporangial production. Furthermore, the population occurring at the lowest salinity (3.6 practical salinity units, psu) did not produce spores. The size of the tetraspores was smaller in the Baltic Sea populations than that in the Irish population, and there were more deformed spores in the Baltic Sea populations than in the Irish populations. Studies with microsatellite markers indicated that clonality is a common phenomenon in the Baltic Sea populations of F. lumbricalis, although the proportion of clonal individuals varied among populations. Some genetic divergence occurred within locations both in Ireland and in the northern Baltic Sea. Even though no carpogonia were detected in the field samples during the study, the microsatellite data indicated that sexual reproduction occurs at least occasionally in the northern Baltic Sea. The genetic diversity of F. lumbricalis was highest in Brittany, France. Since no variation was discovered in the mtDNA cox2-3 spacer sequence, which is generally regarded as an informative phylogeographic marker in red algae, it can be assumed that the studied populations probably share the same origin.

Human genetic variation in the Baltic Sea region: Features of population history and natural selection

In this thesis, the genetic variation of human populations from the Baltic Sea region was studied in order to elucidate population history as well as evolutionary adaptation in this region. The study provided novel understanding of how the complex population level processes of migration, genetic drift, and natural selection have shaped genetic variation in North European populations. Results from genome-wide, mitochondrial DNA and Y-chromosomal analyses suggested that the genetic background of the populations of the Baltic Sea region lies predominantly in Continental Europe, which is consistent with earlier studies and archaeological evidence. The late settlement of Fennoscandia after the Ice Age and the subsequent small population size have led to pronounced genetic drift, especially in Finland and Karelia but also in Sweden, evident especially in genome-wide and Y-chromosomal analyses. Consequently, these populations show striking genetic differentiation, as opposed to much more homogeneous pattern of variation in Central European populations. Additionally, the eastern side of the Baltic Sea was observed to have experienced eastern influence in the genome-wide data as well as in mitochondrial DNA and Y-chromosomal variation – consistent with linguistic connections. However, Slavic influence in the Baltic Sea populations appears minor on genetic level. While the genetic diversity of the Finnish population overall was low, genome-wide and Y-chromosomal results showed pronounced regional differences. The genetic distance between Western and Eastern Finland was larger than for many geographically distant population pairs, and provinces also showed genetic differences. This is probably mainly due to the late settlement of Eastern Finland and local isolation, although differences in ancestral migration waves may contribute to this, too. In contrast, mitochondrial DNA and Y-chromosomal analyses of the contemporary Swedish population revealed a much less pronounced population structure and a fusion of the traces of ancient admixture, genetic drift, and recent immigration. Genome-wide datasets also provide a resource for studying the adaptive evolution of human populations. This study revealed tens of loci with strong signs of recent positive selection in Northern Europe. These results provide interesting targets for future research on evolutionary adaptation, and may be important for understanding the background of disease-causing variants in human populations.