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.

Numerical computation of the module of a quadrilateral

The module of a quadrilateral is a positive real number which divides quadrilaterals into conformal equivalence classes. This is an introductory text to the module of a quadrilateral with some historical background and some numerical aspects. This work discusses the following topics: 1. Preliminaries 2. The module of a quadrilateral 3. The Schwarz-Christoffel Mapping 4. Symmetry properties of the module 5. Computational results 6. Other numerical methods Appendices include: Numerical evaluation of the elliptic integrals of the first kind. Matlab programs and scripts and possible topics for future research. Numerical results section covers additive quadrilaterals and the module of a quadrilateral under the movement of one of its vertex.

Pimeä hehku : Satanismi ja saatananpalvonta 1990-luvun suomalaisessa nuorisokulttuurissa

Satanism in the Finnish Youth Culture of the 1990s The aim of this study was to investigate Satanism among Finnish youth in the 1990s. Thematic interviews of young Finnish Satanists are the basic material of this study. The research employs a theoretical framework derived from narrative psychology and the role-theoretical thinking of Dan P. McAdams. The young Satanists in Finland have been divided into two different groups: the criminal and drug using "devil-worshipping gangs"; and the more educated and philosophically oriented "Satanists" (Heino 1993). What can we say about this division? In the 1990s around Finland, there were young people calling themselves as devil- worshippers (either singular or in groups). They were strongly committed to a mythical devilish and cosmic battle, which they believed was going on in this world. They had problems with their mental health, also in their family socialization and peer groups. In their personal attitudes they were either active fighters or passive tramps. There were also rationally oriented young Satanists, that were ritually active and mainly atheistic. They strongly expressed their personal experiences of being individual and of being different than others. In their personal attitudes they were critical fighters and active survivors. They saw their lives through the satanistic 'finding-oneself experience'. They understood themselves as a "postmodern tribe" (Michel Maffesoli's sosiocultural concept): their sense of themselves was that of a dynamic collectivity which is social, dynamic, nonlocal and mythically historical. Death and black metal culture in the 1990s formed a common space for youth culture, where young individuals could work out their feelings and express their attitudes to life using dark satanic themes and symbols. The sense of "otherness" (also other than satanic) and collective demands for authenticity were essential tools that were used for identity work here. Personal disengagement from satanic/satanistic groups were observed to be gradual or quite rapid. Religious conversions back-and-forth also accured. At the end of the 1990s all off satanism in Finland bore a negative devil-worshipping stigma. Ritual homicide in South-Finland (Kerava/Hyvinkää) was connected to Satanism, which then became unpopular both in the personal life stories and alternative youth cultural circles at the beginning of the 2000s.

Differentiation of neural stem cells in fragile X syndrome

Multipotent stem cells can self-renew and give rise to multiple cell types. One type of mammalian multipotent stem cells are neural stem cells (NSC)s, which can generate neurons, astrocytes and oligodendrocytes. NSCs are likely involved in learning and memory, but their exact role in cognitive function in the developing and adult brain is unclear. We have studied properties of NSCs in fragile X syndrome (FXS), which is the most common form of inherited mental retardation. FXS is caused by the lack of functional fragile X mental retardation protein (FMRP). FMRP is involved in the regulation of postsynaptic protein synthesis in a group I metabotropic glutamate receptor 5 (mGluR5)-dependent manner. In the absence of functional FMRP, the formation of functional synapses is impaired in the forebrain which results in alterations in synaptic plasticity. In our studies, we found that FMRP-deficient NSCs generated more neurons and less glia than control NSCs. The newborn neurons derived from FMRP-deficient NSCs showed an abnormally immature morphology. Furthermore, FMRP-deficient NSCs exhibited aberrant oscillatory Ca2+ responses to glutamate, which were specifically abolished by an antagonist of the mGluR5 receptor. The data suggested alterations in glutamatergic differentiation of FMRP-deficient NSCs and were further supported by an accumulation of cells committed to glutamatergic lineage in the subventricular zone of the embryonic Fmr1-knockout (Fmr1-KO) neocortex. Postnatally, the aberrant cells likely contributed to abnormal formation of the neocortex. The findings suggested a defect in the differentiation of distinct glutamatergic mGluR5 responsive cells in the absence of functional FMRP. Furthermore, we found that in the early postnatal Fmr1-KO mouse brain, the expression of mRNA for regulator of G-protein signalling-4 (RGS4) was decreased which was in line with disturbed G-protein signalling in NSCs lacking FMRP. Brain derived neurotrophic factor (BDNF) promotes neuronal differentiation of NSCs as the absence of FMRP was shown to do. This led us to study the effect of impaired BDNF/TrkB receptor signaling on NSCs by overexpression of TrkB.T1 receptor isoform. We showed that changes in the relative expression levels of the full-length and truncated TrkB isoforms influenced the replication capacity of NSCs. After the differentiation, the overexpression of TrkB.T1 increased neuronal turnover. To summarize, FMRP and TrkB signaling are involved in normal differentiation of NSCs in the developing brain. Since NSCs might have potential for therapeutic interventions in a variety of neurological disorders, our findings may be useful in the design of pharmacological interventions in neurological disorders of learning and memory.

Cardiac function before and after treatment for various types of loading conditions and in myocardial restriction : A prospective study on pediatric patients with two- and three-dimensional echocardiography and measurement of serum natriuretic peptides

Background: The incidence of all forms of congenital heart defects is 0.75%. For patients with congenital heart defects, life-expectancy has improved with new treatment modalities. Structural heart defects may require surgical or catheter treatment which may be corrective or palliative. Even those with corrective therapy need regular follow-up due to residual lesions, late sequelae, and possible complications after interventions. Aims: The aim of this thesis was to evaluate cardiac function before and after treatment for volume overload of the right ventricle (RV) caused by atrial septal defect (ASD), volume overload of the left ventricle (LV) caused by patent ductus arteriosus (PDA), and pressure overload of the LV caused by coarctation of the aorta (CoA), and to evaluate cardiac function in patients with Mulibrey nanism. Methods: In Study I, of the 24 children with ASD, 7 underwent surgical correction and 17 percutaneous occlusion of ASD. Study II had 33 patients with PDA undergoing percutaneous occlusion. In Study III, 28 patients with CoA underwent either surgical correction or percutaneous balloon dilatation of CoA. Study IV comprised 26 children with Mulibrey nanism. A total of 76 healthy voluntary children were examined as a control group. In each study, controls were matched to patients. All patients and controls underwent clinical cardiovascular examinations, two-dimensional (2D) and three-dimensional (3D) echocardiographic examinations, and blood sampling for measurement of natriuretic peptides prior to the intervention and twice or three times thereafter. Control children were examined once by 2D and 3D echocardiography. M-mode echocardiography was performed from the parasternal long axis view directed by 2D echocardiography. The left atrium-to-aorta (LA/Ao) ratio was calculated as an index of LA size. The end-diastolic and end-systolic dimensions of LV as well as the end-diastolic thicknesses of the interventricular septum and LV posterior wall were measured. LV volumes, and the fractional shortening (FS) and ejection fraction (EF) as indices of contractility were then calculated, and the z scores of LV dimensions determined. Diastolic function of LV was estimated from the mitral inflow signal obtained by Doppler echocardiography. In three-dimensional echocardiography, time-volume curves were used to determine end-diastolic and end-systolic volumes, stroke volume, and EF. Diastolic and systolic function of LV was estimated from the calculated first derivatives of these curves. Results: (I): In all children with ASD, during the one-year follow-up, the z score of the RV end-diastolic diameter decreased and that of LV increased. However, dilatation of RV did not resolve entirely during the follow-up in either treatment group. In addition, the size of LV increased more slowly in the surgical subgroup but reached control levels in both groups. Concentrations of natriuretic peptides in patients treated percutaneously increased during the first month after ASD closure and normalized thereafter, but in patients treated surgically, they remained higher than in controls. (II): In the PDA group, at baseline, the end-diastolic diameter of LV measured over 2SD in 5 of 33 patients. The median N-terminal pro-brain natriuretic peptide (proBNP) concentration before closure measured 72 ng/l in the control group and 141 ng/l in the PDA group (P = 0.001) and 6 months after closure measured 78.5 ng/l (P = NS). Patients differed from control subjects in indices of LV diastolic and systolic function at baseline, but by the end of follow-up, all these differences had disappeared. Even in the subgroup of patients with normal-sized LV at baseline, the LV end-diastolic volume decreased significantly during follow-up. (III): Before repair, the size and wall thickness of LV were higher in patients with CoA than in controls. Systolic blood pressure measured a median 123 mm Hg in patients before repair (P < 0.001) and 103 mm Hg one year thereafter, and 101 mm Hg in controls. The diameter of the coarctation segment measured a median 3.0 mm at baseline, and 7.9 at the 12-month (P = 0.006) follow-up. Thicknesses of the interventricular septum and posterior wall of the LV decreased after repair but increased to the initial level one year thereafter. The velocity time integrals of mitral inflow increased, but no changes were evident in LV dimensions or contractility. During follow-up, serum levels of natriuretic peptides decreased correlating with diastolic and systolic indices of LV function in 2D and 3D echocardiography. (IV): In 2D echocardiography, the interventricular septum and LV posterior wall were thicker, and velocity time integrals of mitral inflow shorter in patients with Mulibrey nanism than in controls. In 3D echocardiography, LV end-diastolic volume measured a median 51.9 (range 33.3 to 73.4) ml/m² in patients and 59.7 (range 37.6 to 87.6) ml/m² in controls (P = 0.040), and serum levels of ANPN and proBNP a median 0.54 (range 0.04 to 4.7) nmol/l and 289 (range 18 to 9170) ng/l, in patients and 0.28 (range 0.09 to 0.72) nmol/l (P < 0.001) and 54 (range 26 to 139) ng/l (P < 0.001) in controls. They correlated with several indices of diastolic LV function. Conclusions (I): During the one-year follow-up after the ASD closure, RV size decreased but did not normalize in all patients. The size of the LV normalized after ASD closure but the increase in LV size was slower in patients treated surgically than in those treated with the percutaneous technique. Serum levels of ANPN and proBNP were elevated prior to ASD closure but decreased thereafter to control levels in patients treated with the percutaneous technique but not in those treated surgically. (II): Changes in LV volume and function caused by PDA disappeared by 6 months after percutaneous closure. Even the children with normal-sized LV benefited from the procedure. (III): After repair of CoA, the RV size and the velocity time integrals of mitral inflow increased, and serum levels of natriuretic peptides decreased. Patients need close follow-up, despite cessation of LV pressure overload, since LV hypertrophy persisted even in normotensive patients with normal growth of the coarctation segment. (IV): In children with Mulibrey nanism, the LV wall was hypertrophied, with myocardial restriction and impairment of LV function. Significant correlations appeared between indices of LV function, size of the left atrium, and levels of natriuretic peptides, indicating that measurement of serum levels of natriuretic peptides can be used in the clinical follow-up of this patient group despite its dependence on loading conditions.

Eron aika : Tyttärien kertomuksia ikääntyneen vanhemman kuolemasta

There is a relative absence of sociological and cultural research on how people deal with the death of a family member in the contemporary western societies. Research on this topic has been dominated by the experts of psychology, psychiatry and therapy, who mention the social context only in passing, if at all. This gives an impression that the white westerners bereavement experience is a purely psychological phenomenon, an inner journey, which follows a natural, universal path. Yet, as Tony Walter (1999) states, ignoring the influence of culture not only impoverishes the understanding of those work with bereaved people, but it also impoverishes sociology and cultural studies by excluding from their domain a key social phenomenon. This study explores the cultural dimension of grief through narratives told by fifteen of recently bereaved Finnish women. Focussing on one sex only, the study rests on the assumption of the gendered nature of bereavement experience. However, the aim of the study is not to pinpoint the gender differences in grief and mourning, but to shed light on women s ways of dealing with the loss of a loved one in a social context. Furthermore, the study focuses on a certain kind of loss: the death of an elderly parent. Due to the growth in the life expectancy rate, this has presumably become the most typical type of bereavement in contemporary, ageing societies. Most of population will face the death of a parent as they reach the middle years of the life course. The data of this study is gathered with interviews, in which the interviewees were invited to tell a narrative of their bereavement. Narrative constitutes a central concept in this study. It refers to a particular form of talk, which is organised around consequential events. But there are also other, deeper layers that have been added to this concept. Several scholars see narratives as the most important way in which we make sense of experience. Personal narratives provide rich material for mapping the interconnections between individual and culture. As a form of thought, narrative marries singular circumstances with shared expectations and understandings that are learned through participation in a specific culture (Garro & Mattingly 2000). This study attempts to capture the cultural dimension of narrative with the concept of script , which originates in cognitive science (Schank & Abelson 1977) and has recently been adopted to narratology (Herman 2002). Script refers to a data structure that informs how events usually unfold in certain situations. Scripts are used in interpreting events and representing them verbally to others. They are based on dominant forms of knowledge that vary according to time and place. The questions that were posed in this study are the following. What kind of experiences bereaved daughters narrate? What kind of cultural scripts they employ as they attempt to make sense of these experiences? How these scripts are used in their narratives? It became apparent that for the most of the daughters interviewed in this study the single most important part of the bereavement narrative was to form an account of how and why the parent died. They produced lengthy and detailed descriptions of the last stage of a parent s life in contrast with the rest of the interview. These stories took their start from a turn in the parent s physical condition, from which the dying process could in retrospect be seen to have started, and which often took place several years before the death. In addition, daughters also talked about their grief reactions and how they have adjusted to a life without the deceased parent. The ways in which the last stage of life was told reflect not only the characteristic features of late modernity but also processes of marginalisation and exclusion. Revivalist script and medical script, identified by Clive Seale as the dominant, competing models for dying well in the late modern societies, were not widely utilised in the narratives. They could only be applied in situations in which the parent had died from cancer and at somewhat younger age than the average. Death that took place in deep old age was told in a different way. The lack of positive models for narrating this kind of death was acknowledged in the study. This can be seen as a symptom of the societal devaluing of the deaths of older people and it affects also daughters accounts of their grief. Several daughters told about situations in which their loss, although subjectively experienced, was nonetheless denied by other people.

Direct and Inverse Scattering for Beltrami Fields

We consider an obstacle scattering problem for linear Beltrami fields. A vector field is a linear Beltrami field if the curl of the field is a constant times itself. We study the obstacles that are of Neumann type, that is, the normal component of the total field vanishes on the boundary of the obstacle. We prove the unique solvability for the corresponding exterior boundary value problem, in other words, the direct obstacle scattering model. For the inverse obstacle scattering problem, we deduce the formulas that are needed to apply the singular sources method. The numerical examples are computed for the direct scattering problem and for the inverse scattering problem.

Coherent quantum Boltzmann equations from cQPA

We reformulate and extend our recently introduced quantum kinetic theory for interacting fermion and scalar fields. Our formalism is based on the coherent quasiparticle approximation (cQPA) where nonlocal coherence information is encoded in new spectral solutions at off-shell momenta. We derive explicit forms for the cQPA propagators in the homogeneous background and show that the collision integrals involving the new coherence propagators need to be resummed to all orders in gradient expansion. We perform this resummation and derive generalized momentum space Feynman rules including coherent propagators and modified vertex rules for a Yukawa interaction. As a result we are able to set up self-consistent quantum Boltzmann equations for both fermion and scalar fields. We present several examples of diagrammatic calculations and numerical applications including a simple toy model for coherent baryogenesis.

Global, Local and Vector-Valued Tb Theorems on Non-Homogeneous Metric Spaces

Various Tb theorems play a key role in the modern harmonic analysis. They provide characterizations for the boundedness of Calderón-Zygmund type singular integral operators. The general philosophy is that to conclude the boundedness of an operator T on some function space, one needs only to test it on some suitable function b. The main object of this dissertation is to prove very general Tb theorems. The dissertation consists of four research articles and an introductory part. The framework is general with respect to the domain (a metric space), the measure (an upper doubling measure) and the range (a UMD Banach space). Moreover, the used testing conditions are weak. In the first article a (global) Tb theorem on non-homogeneous metric spaces is proved. One of the main technical components is the construction of a randomization procedure for the metric dyadic cubes. The difficulty lies in the fact that metric spaces do not, in general, have a translation group. Also, the measures considered are more general than in the existing literature. This generality is genuinely important for some applications, including the result of Volberg and Wick concerning the characterization of measures for which the analytic Besov-Sobolev space embeds continuously into the space of square integrable functions. In the second article a vector-valued extension of the main result of the first article is considered. This theorem is a new contribution to the vector-valued literature, since previously such general domains and measures were not allowed. The third article deals with local Tb theorems both in the homogeneous and non-homogeneous situations. A modified version of the general non-homogeneous proof technique of Nazarov, Treil and Volberg is extended to cover the case of upper doubling measures. This technique is also used in the homogeneous setting to prove local Tb theorems with weak testing conditions introduced by Auscher, Hofmann, Muscalu, Tao and Thiele. This gives a completely new and direct proof of such results utilizing the full force of non-homogeneous analysis. The final article has to do with sharp weighted theory for maximal truncations of Calderón-Zygmund operators. This includes a reduction to certain Sawyer-type testing conditions, which are in the spirit of Tb theorems and thus of the dissertation. The article extends the sharp bounds previously known only for untruncated operators, and also proves sharp weak type results, which are new even for untruncated operators. New techniques are introduced to overcome the difficulties introduced by the non-linearity of maximal truncations.

A maximal operator, Carleson's embedding, and tent spaces for vector-valued functions

This thesis is concerned with the area of vector-valued Harmonic Analysis, where the central theme is to determine how results from classical Harmonic Analysis generalize to functions with values in an infinite dimensional Banach space. The work consists of three articles and an introduction. The first article studies the Rademacher maximal function that was originally defined by T. Hytönen, A. McIntosh and P. Portal in 2008 in order to prove a vector-valued version of Carleson's embedding theorem. The boundedness of the corresponding maximal operator on Lebesgue-(Bochner) -spaces defines the RMF-property of the range space. It is shown that the RMF-property is equivalent to a weak type inequality, which does not depend for instance on the integrability exponent, hence providing more flexibility for the RMF-property. The second article, which is written in collaboration with T. Hytönen, studies a vector-valued Carleson's embedding theorem with respect to filtrations. An earlier proof of the dyadic version assumed that the range space satisfies a certain geometric type condition, which this article shows to be also necessary. The third article deals with a vector-valued generalizations of tent spaces, originally defined by R. R. Coifman, Y. Meyer and E. M. Stein in the 80's, and concerns especially the ones related to square functions. A natural assumption on the range space is then the UMD-property. The main result is an atomic decomposition for tent spaces with integrability exponent one. In order to suit the stochastic integrals appearing in the vector-valued formulation, the proof is based on a geometric lemma for cones and differs essentially from the classical proof. Vector-valued tent spaces have also found applications in functional calculi for bisectorial operators. In the introduction these three themes come together when studying paraproduct operators for vector-valued functions. The Rademacher maximal function and Carleson's embedding theorem were applied already by Hytönen, McIntosh and Portal in order to prove boundedness for the dyadic paraproduct operator on Lebesgue-Bochner -spaces assuming that the range space satisfies both UMD- and RMF-properties. Whether UMD implies RMF is thus an interesting question. Tent spaces, on the other hand, provide a method to study continuous time paraproduct operators, although the RMF-property is not yet understood in the framework of tent spaces.

Cohésion modale et subordination : Le conditionnel et le jussif finnois au miroir de la valeur sémantique et discursive du subjonctif français

Modal cohesion and subordination. The Finnish conditional and jussive moods in comparison to the French subjunctive This study examines verb moods in subordinate clauses in French and Finnish. The first part of the analysis deals with the syntax and semantics of the French subjunctive, mood occurring mostly in subordinate positions. The second part investigates Finnish verb moods. Although subordinate positions in Finnish grammar have no special finite verb form, certain uses of Finnish verb moods have been compared to those of subjunctives and conjunctives in other languages. The present study focuses on the subordinate uses of the Finnish conditional and jussive (i.e. the third person singular and plural of the imperative mood). The third part of the analysis discusses the functions of subordinate moods in contexts beyond complex sentences. The data used for the analysis include 1834 complex sentences gathered from newspapers, online discussion groups and blog texts, as well as audio-recorded interviews and conversations. The data thus consist of both written and oral texts as well as standard and non-standard variants. The analysis shows that the French subjunctive codes theoretical modality. The subjunctive does not determine the temporal and modal meaning of the event, but displays the event as virtual. In a complex sentence, the main clause determines the temporal and modal space within which the event coded by the subjunctive clause is interpreted. The subjunctive explicitly indicates that the space constructed in the main clause extends its scope over the subordinate clause. The subjunctive can therefore serve as a means for creating modal cohesion in the discourse. The Finnish conditional shares the function of making explicit the modal link between the components of a complex construction with the French subjunctive, but the two moods differ in their semantics. The conditional codes future time and can therefore occur only in non-factual or counterfactual contexts, whereas the event expressed by French subjunctive clauses can also be interpreted as realized. Such is the case when, for instance, generic and habitual meaning is involved. The Finnish jussive mood is used in a relatively limited number of subordinate clause types, but in these contexts its modal meaning is strikingly close to that of the French subjunctive. The permissive meaning, typical of the jussive in main clause positions, is modified in complex sentences so that it entails inter-clausal relation, namely concession. Like the French subjunctive, the jussive codes theoretical modal meaning with no implication of the truth value of the proposition. Finally, the analysis shows that verb moods mark modal cohesion, not only on the syntagmatic level (namely in complexe sentences), but also on the paradigmatic axis of discourse in order to create semantic links over entire segments of talk. In this study, the subjunctive thus appears, not as an empty category without function, as it is sometimes described, but as an open form that conveys the temporal and modal meanings emerging from the context.