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.

Gene flow from transgenic plant populations: models and applications for risk assessment

The future use of genetically modified (GM) plants in food, feed and biomass production requires a careful consideration of possible risks related to the unintended spread of trangenes into new habitats. This may occur via introgression of the transgene to conventional genotypes, due to cross-pollination, and via the invasion of GM plants to new habitats. Assessment of possible environmental impacts of GM plants requires estimation of the level of gene flow from a GM population. Furthermore, management measures for reducing gene flow from GM populations are needed in order to prevent possible unwanted effects of transgenes on ecosystems. This work develops modeling tools for estimating gene flow from GM plant populations in boreal environments and for investigating the mechanisms of the gene flow process. To describe spatial dimensions of the gene flow, dispersal models are developed for the local and regional scale spread of pollen grains and seeds, with special emphasis on wind dispersal. This study provides tools for describing cross-pollination between GM and conventional populations and for estimating the levels of transgenic contamination of the conventional crops. For perennial populations, a modeling framework describing the dynamics of plants and genotypes is developed, in order to estimate the gene flow process over a sequence of years. The dispersal of airborne pollen and seeds cannot be easily controlled, and small amounts of these particles are likely to disperse over long distances. Wind dispersal processes are highly stochastic due to variation in atmospheric conditions, so that there may be considerable variation between individual dispersal patterns. This, in turn, is reflected to the large amount of variation in annual levels of cross-pollination between GM and conventional populations. Even though land-use practices have effects on the average levels of cross-pollination between GM and conventional fields, the level of transgenic contamination of a conventional crop remains highly stochastic. The demographic effects of a transgene have impacts on the establishment of trangenic plants amongst conventional genotypes of the same species. If the transgene gives a plant a considerable fitness advantage in comparison to conventional genotypes, the spread of transgenes to conventional population can be strongly increased. In such cases, dominance of the transgene considerably increases gene flow from GM to conventional populations, due to the enhanced fitness of heterozygous hybrids. The fitness of GM plants in conventional populations can be reduced by linking the selectively favoured primary transgene to a disfavoured mitigation transgene. Recombination between these transgenes is a major risk related to this technique, especially because it tends to take place amongst the conventional genotypes and thus promotes the establishment of invasive transgenic plants in conventional populations.

Computational Methods for Detecting Large-Scale Chromosome Rearrangements in SNP Data

Large-scale chromosome rearrangements such as copy number variants (CNVs) and inversions encompass a considerable proportion of the genetic variation between human individuals. In a number of cases, they have been closely linked with various inheritable diseases. Single-nucleotide polymorphisms (SNPs) are another large part of the genetic variance between individuals. They are also typically abundant and their measuring is straightforward and cheap. This thesis presents computational means of using SNPs to detect the presence of inversions and deletions, a particular variety of CNVs. Technically, the inversion-detection algorithm detects the suppressed recombination rate between inverted and non-inverted haplotype populations whereas the deletion-detection algorithm uses the EM-algorithm to estimate the haplotype frequencies of a window with and without a deletion haplotype. As a contribution to population biology, a coalescent simulator for simulating inversion polymorphisms has been developed. Coalescent simulation is a backward-in-time method of modelling population ancestry. Technically, the simulator also models multiple crossovers by using the Counting model as the chiasma interference model. Finally, this thesis includes an experimental section. The aforementioned methods were tested on synthetic data to evaluate their power and specificity. They were also applied to the HapMap Phase II and Phase III data sets, yielding a number of candidates for previously unknown inversions, deletions and also correctly detecting known such rearrangements.

Short-term effects of variable retention on epigaeic spiders and carabid beetles in Finland

Forestry has influenced forest dwelling organisms for centuries in Fennoscandia. For example, in Finland ca. 30% of the threatened species are threatened because of forestry. Nowadays forest management recommendations include practices aimed at maintaining biodiversity in harvesting, such as green-tree retention. However, the effects of these practices have been little studied. In variable retention, different numbers of trees are retained, varying from green-tree retention (at least a few live standing trees in clear-cuts) to thinning (only individual trees removed). I examined the responses of ground-dwelling spiders and carabid beetles to green-tree retention (with small and large tree groups), gap felling and thinning aimed at an uneven age structure of trees. The impacts of these harvesting methods were compared to those of clear-cutting and uncut controls. I aimed to test the hypothesis that retaining more trees positively affects populations of those species of spiders and carabids that were present before harvesting. The data come from two studies. First, spiders were collected with pitfall traps in south-central Finland in 1995 (pre-treatment) and 1998 (after-treatment) in order to examine the effects of clear-cutting, green-tree retention (with 0.01-0.02-ha sized tree groups), gap felling (with three 0.16-ha sized openings in a 1-ha stand), thinning aiming at an uneven age structure of trees and uncut control. Second, spiders and carabids were caught with pitfall traps in eastern Finland in 1998-2001 (pre-treatment and three post-treatment years) in eleven 0.09-0.55-ha sized retention-tree groups and clear-cuts adjacent to them. Original spider and carabid assemblages were better maintained after harvests that retained more trees. Thinning maintained forest spiders well. However, gap felling and large retention-tree groups maintained some forest spider and carabid species in the short-term, but negatively affected some species over time. However, use of small retention-tree groups was associated with negative effects on forest spider populations. Studies are needed on the long-term effects of variable retention on terrestrial invertebrates; especially those directed at defining appropriate retention patch size and on the importance of structural diversity provided by variable retention for invertebrate populations. However, the aims of variable retention should be specified first. For example, are retention-tree groups planned to constitute life-boats , stepping-stones or to create structural diversity? Does it suffice that some species are maintained, or do we want to preserve the most sensitive ones, and how are these best defined? Moreover, the ecological benefits and economic costs of modified logging methods should be compared to other approaches aimed at maintaining biodiversity.

Characterisation and source identification of pollution episodes caused by long-range transported aerosols

Aerosol particles can cause detrimental environmental and health effects. The particles and their precursor gases are emitted from various anthropogenic and natural sources. It is important to know the origin and properties of aerosols to efficiently reduce their harmful effects. The diameter of aerosol particles (Dp) varies between ~0.001 and ~100 μm. Fine particles (PM2.5: Dp < 2.5 μm) are especially interesting because they are the most harmful and can be transported over long distances. The aim of this thesis is to study the impact on air quality by pollution episodes of long-range transported aerosols affecting the composition of the boundary-layer atmosphere in remote and relatively unpolluted regions of the world. The sources and physicochemical properties of aerosols were investigated in detail, based on various measurements (1) in southern Finland during selected long-range transport (LRT) pollution episodes and unpolluted periods and (2) over the Atlantic Ocean between Europe and Antarctica during a voyage. Furthermore, the frequency of LRT pollution episodes of fine particles in southern Finland was investigated over a period of 8 years, using long-term air quality monitoring data. In southern Finland, the annual mean PM2.5 mass concentrations were low but LRT caused high peaks of daily mean concentrations every year. At an urban background site in Helsinki, the updated WHO guideline value (24-h PM2.5 mean 25 μg/m3) was exceeded during 1-7 LRT episodes each year during 1999-2006. The daily mean concentrations varied between 25 and 49 μg/m3 during the episodes, which was 3-6 times higher than the mean concentration in the long term. The in-depth studies of selected LRT episodes in southern Finland revealed that biomass burning in agricultural fields and wildfires, occurring mainly in Eastern Europe, deteriorated air quality on a continental scale. The strongest LRT episodes of fine particles resulted from open biomass-burning fires but the emissions from other anthropogenic sources in Eastern Europe also caused significant LRT episodes. Particle mass and number concentrations increased strongly in the accumulation mode (Dp ~ 0.09-1 μm) during the LRT episodes. However, the concentrations of smaller particles (Dp < 0.09 μm) remained low or even decreased due to the uptake of vapours and molecular clusters by LRT particles. The chemical analysis of individual particles showed that the proportions of several anthropogenic particle types increased (e.g. tar balls, metal oxides/hydroxides, spherical silicate fly ash particles and various calcium-rich particles) in southern Finland during an LRT episode, when aerosols originated from the polluted regions of Eastern Europe and some open biomass-burning smoke was also brought in by LRT. During unpolluted periods when air masses arrived from the north, the proportions of marine aerosols increased. In unpolluted rural regions of southern Finland, both accumulation mode particles and small-sized (Dp ~ 1-3 μm) coarse mode particles originated mostly from LRT. However, the composition of particles was totally different in these size fractions. In both size fractions, strong internal mixing of chemical components was typical for LRT particles. Thus, the aging of particles has significant impacts on their chemical, hygroscopic and optical properties, which can largely alter the environmental and health effects of LRT aerosols. Over the Atlantic Ocean, the individual particle composition of small-sized (Dp ~ 1-3 μm) coarse mode particles was affected by continental aerosol plumes to distances of at least 100-1000 km from the coast (e.g. pollutants from industrialized Europe, desert dust from the Sahara and biomass-burning aerosols near the Gulf of Guinea). The rate of chloride depletion from sea-salt particles was high near the coasts of Europe and Africa when air masses arrived from polluted continental regions. Thus, the LRT of continental aerosols had significant impacts on the composition of the marine boundary-layer atmosphere and seawater. In conclusion, integration of the results obtained using different measurement techniques captured the large spatial and temporal variability of aerosols as observed at terrestrial and marine sites, and assisted in establishing the causal link between land-bound emissions, LRT and air quality.

Ecological impacts of Phlebiopsis gigantea biocontrol treatment against Heterobasidion spp. as revealed by fungal community profiling and population analyses

Wood decay fungi belonging to the species complex Heterobasidion annosum sensu lato are among the most common and economically important species causing root rot and stem decay in conifers of the northern temperate regions. New infections by these pathogens can be suppressed by tree stump treatments using chemical or biological control agents. In Finland, the corticiaceous fungus Phlebiopsis gigantea has been formulated into a commercial biocontrol agent called Rotstop (Verdera Ltd.). This thesis addresses the ecological impacts of Rotstop biocontrol treatment on the mycoflora of conifer stumps. Locally, fungal communities within Rotstop-treated and untreated stumps were analyzed using a novel method based on DGGE profiling of small subunit ribosomal DNA fragments amplified directly from wood samples. Population analyses for P. gigantea and H. annosum s.l. were conducted to evaluate possible risks associated with local and/or global distribution of the Rotstop strain. Based on molecular community profiling by DGGE, we detected a few individual wood-inhabiting fungal species (OTUs) that seemed to have suffered or benefited from the Rotstop biocontrol treatment. The DGGE analyses also revealed fungal diversity not retrieved by cultivation and some fungal sequence types untypical for decomposing conifer wood. However, statistical analysis of DGGE community profiles obtained from Rotstop-treated and untreated conifer stumps revealed that the Rotstop treatment had not caused a statistically significant reduction in the species diversity of wood-inhabiting fungi within our experimental forest plots. Locally, ISSR genotyping of cultured P. gigantea strains showed that the Rotstop biocontrol strain was capable of surviving up to six years within treated Norway spruce stumps, while in Scots pine stumps it was sooner replaced by successor fungal species. In addition, the spread of resident P. gigantea strains into Rotstop-treated forest stands seemed effective in preventing the formation of genetically monomorphic populations in the short run. On a global scale, we detected a considerable level of genetic differentiation between the interfertile European and North American populations of P. gigantea. These results strongly suggest that local biocontrol strains should be used in order to prevent global spread of P. gigantea and hybrid formation between geographically isolated populations. The population analysis for H. annosum s.l. revealed a collection of Chinese fungal strains that showed a high degree of laboratory fertility with three different allopatric H. annosum s.l. taxa. However, based on the molecular markers, the Chinese strains could be clearly affiliated with the H. parviporum taxonomical cluster, which thus appears to have a continuous distribution range from Europe through southern Siberia to northern China. Keywords: Rotstop, wood decay, DGGE, ISSR fingerprinting, ribosomal DNA

The Gerbera cDNA Microarray: A Tool for Large-Scale Identification of Genes Involved in Flower Development

During the past ten years, large-scale transcript analysis using microarrays has become a powerful tool to identify and predict functions for new genes. It allows simultaneous monitoring of the expression of thousands of genes and has become a routinely used tool in laboratories worldwide. Microarray analysis will, together with other functional genomics tools, take us closer to understanding the functions of all genes in genomes of living organisms. Flower development is a genetically regulated process which has mostly been studied in the traditional model species Arabidopsis thaliana, Antirrhinum majus and Petunia hybrida. The molecular mechanisms behind flower development in them are partly applicable in other plant systems. However, not all biological phenomena can be approached with just a few model systems. In order to understand and apply the knowledge to ecologically and economically important plants, other species also need to be studied. Sequencing of 17 000 ESTs from nine different cDNA libraries of the ornamental plant Gerbera hybrida made it possible to construct a cDNA microarray with 9000 probes. The probes of the microarray represent all different ESTs in the database. From the gerbera ESTs 20% were unique to gerbera while 373 were specific to the Asteraceae family of flowering plants. Gerbera has composite inflorescences with three different types of flowers that vary from each other morphologically. The marginal ray flowers are large, often pigmented and female, while the central disc flowers are smaller and more radially symmetrical perfect flowers. Intermediate trans flowers are similar to ray flowers but smaller in size. This feature together with the molecular tools applied to gerbera, make gerbera a unique system in comparison to the common model plants with only a single kind of flowers in their inflorescence. In the first part of this thesis, conditions for gerbera microarray analysis were optimised including experimental design, sample preparation and hybridization, as well as data analysis and verification. Moreover, in the first study, the flower and flower organ-specific genes were identified. After the reliability and reproducibility of the method were confirmed, the microarrays were utilized to investigate transcriptional differences between ray and disc flowers. This study revealed novel information about the morphological development as well as the transcriptional regulation of early stages of development in various flower types of gerbera. The most interesting finding was differential expression of MADS-box genes, suggesting the existence of flower type-specific regulatory complexes in the specification of different types of flowers. The gerbera microarray was further used to profile changes in expression during petal development. Gerbera ray flower petals are large, which makes them an ideal model to study organogenesis. Six different stages were compared and specifically analysed. Expression profiles of genes related to cell structure and growth implied that during stage two, cells divide, a process which is marked by expression of histones, cyclins and tubulins. Stage 4 was found to be a transition stage between cell division and expansion and by stage 6 cells had stopped division and instead underwent expansion. Interestingly, at the last analysed stage, stage 9, when cells did not grow any more, the highest number of upregulated genes was detected. The gerbera microarray is a fully-functioning tool for large-scale studies of flower development and correlation with real-time RT-PCR results show that it is also highly sensitive and reliable. Gene expression data presented here will be a source for gene expression mining or marker gene discovery in the future studies that will be performed in the Gerbera Laboratory. The publicly available data will also serve the plant research community world-wide.

Maintaining plant species richness by cattle grazing - mesic semi-natural grasslands as focal habitats

Semi-natural grasslands are the most important agricultural areas for biodiversity. The present study investigates the effects of traditional livestock grazing and mowing on plant species richness, the main emphasis being on cattle grazing in mesic semi-natural grasslands. The two reviews provide a thorough assessment of the multifaceted impacts and importance of grazing and mowing management to plant species richness. It is emphasized that livestock grazing and mowing have partially compensated the suppression of major natural disturbances by humans and mitigated the negative effects of eutrophication. This hypothesis has important consequences for nature conservation: A large proportion of European species originally adapted to natural disturbances may be at present dependent on livestock grazing and / or mowing. Furthermore, grazing and mowing are key management methods to mitigate effects of nutrient-enrichment. The species composition and richness in old (continuously grazed), new (grazing restarting 3-8 years ago) and abandoned (over 10 years) pastures differed consistently across a range of spatial scales, and was intermediate in new pastures compared to old and abandoned pastures. In mesic grasslands most plant species were shown to benefit from cattle grazing. Indicator species of biologically valuable grasslands and rare species were more abundant in grazed than in abandoned grasslands. Steep S-SW-facing slopes are the most suitable sites for many grassland plants and should be prioritized in grassland restoration. The proportion of species trait groups benefiting from grazing was higher in mesic semi-natural grasslands than in dry and wet grasslands. Consequently, species trait responses to grazing and the effectiveness of the natural factors limiting plant growth may be intimately linked High plant species richness of traditionally mowed and grazed areas is explained by numerous factors which operate on different spatial scales. Particularly important for maintaining large scale plant species richness are evolutionary and mitigation factors. Grazing and mowing cause a shift towards the conditions that have occurred during the evolutionary history of European plant species by modifying key ecological factors (nutrients, pH and light). The results of this Dissertation suggest that restoration of semi-natural grasslands by private farmers is potentially a useful method to manage biodiversity in the agricultural landscape. However, the quality of management is commonly improper, particularly due to financial constraints. For enhanced success of restoration, management regulations in the agri-environment scheme need to be defined more explicitly and the scheme should be revised to encourage management of biodiversity.