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.

Semantic Classes in Topic Detection and Tracking

Topic detection and tracking (TDT) is an area of information retrieval research the focus of which revolves around news events. The problems TDT deals with relate to segmenting news text into cohesive stories, detecting something new, previously unreported, tracking the development of a previously reported event, and grouping together news that discuss the same event. The performance of the traditional information retrieval techniques based on full-text similarity has remained inadequate for online production systems. It has been difficult to make the distinction between same and similar events. In this work, we explore ways of representing and comparing news documents in order to detect new events and track their development. First, however, we put forward a conceptual analysis of the notions of topic and event. The purpose is to clarify the terminology and align it with the process of news-making and the tradition of story-telling. Second, we present a framework for document similarity that is based on semantic classes, i.e., groups of words with similar meaning. We adopt people, organizations, and locations as semantic classes in addition to general terms. As each semantic class can be assigned its own similarity measure, document similarity can make use of ontologies, e.g., geographical taxonomies. The documents are compared class-wise, and the outcome is a weighted combination of class-wise similarities. Third, we incorporate temporal information into document similarity. We formalize the natural language temporal expressions occurring in the text, and use them to anchor the rest of the terms onto the time-line. Upon comparing documents for event-based similarity, we look not only at matching terms, but also how near their anchors are on the time-line. Fourth, we experiment with an adaptive variant of the semantic class similarity system. The news reflect changes in the real world, and in order to keep up, the system has to change its behavior based on the contents of the news stream. We put forward two strategies for rebuilding the topic representations and report experiment results. We run experiments with three annotated TDT corpora. The use of semantic classes increased the effectiveness of topic tracking by 10-30\% depending on the experimental setup. The gain in spotting new events remained lower, around 3-4\%. The anchoring the text to a time-line based on the temporal expressions gave a further 10\% increase the effectiveness of topic tracking. The gains in detecting new events, again, remained smaller. The adaptive systems did not improve the tracking results.

Cross-layer Assisted TCP Algorithms for Vertical Handoff

The ever expanding growth of the wireless access to the Internet in recent years has led to the proliferation of wireless and mobile devices to connect to the Internet. This has created the possibility of mobile devices equipped with multiple radio interfaces to connect to the Internet using any of several wireless access network technologies such as GPRS, WLAN and WiMAX in order to get the connectivity best suited for the application. These access networks are highly heterogeneous and they vary widely in their characteristics such as bandwidth, propagation delay and geographical coverage. The mechanism by which a mobile device switches between these access networks during an ongoing connection is referred to as vertical handoff and it often results in an abrupt and significant change in the access link characteristics. The most common Internet applications such as Web browsing and e-mail make use of the Transmission Control Protocol (TCP) as their transport protocol and the behaviour of TCP depends on the end-to-end path characteristics such as bandwidth and round-trip time (RTT). As the wireless access link is most likely the bottleneck of a TCP end-to-end path, the abrupt changes in the link characteristics due to a vertical handoff may affect TCP behaviour adversely degrading the performance of the application. The focus of this thesis is to study the effect of a vertical handoff on TCP behaviour and to propose algorithms that improve the handoff behaviour of TCP using cross-layer information about the changes in the access link characteristics. We begin this study by identifying the various problems of TCP due to a vertical handoff based on extensive simulation experiments. We use this study as a basis to develop cross-layer assisted TCP algorithms in handoff scenarios involving GPRS and WLAN access networks. We then extend the scope of the study by developing cross-layer assisted TCP algorithms in a broader context applicable to a wide range of bandwidth and delay changes during a handoff. And finally, the algorithms developed here are shown to be easily extendable to the multiple-TCP flow scenario. We evaluate the proposed algorithms by comparison with standard TCP (TCP SACK) and show that the proposed algorithms are effective in improving TCP behavior in vertical handoff involving a wide range of bandwidth and delay of the access networks. Our algorithms are easy to implement in real systems and they involve modifications to the TCP sender algorithm only. The proposed algorithms are conservative in nature and they do not adversely affect the performance of TCP in the absence of cross-layer information.

Problems and Algorithms for Sequence Segmentations

The analysis of sequential data is required in many diverse areas such as telecommunications, stock market analysis, and bioinformatics. A basic problem related to the analysis of sequential data is the sequence segmentation problem. A sequence segmentation is a partition of the sequence into a number of non-overlapping segments that cover all data points, such that each segment is as homogeneous as possible. This problem can be solved optimally using a standard dynamic programming algorithm. In the first part of the thesis, we present a new approximation algorithm for the sequence segmentation problem. This algorithm has smaller running time than the optimal dynamic programming algorithm, while it has bounded approximation ratio. The basic idea is to divide the input sequence into subsequences, solve the problem optimally in each subsequence, and then appropriately combine the solutions to the subproblems into one final solution. In the second part of the thesis, we study alternative segmentation models that are devised to better fit the data. More specifically, we focus on clustered segmentations and segmentations with rearrangements. While in the standard segmentation of a multidimensional sequence all dimensions share the same segment boundaries, in a clustered segmentation the multidimensional sequence is segmented in such a way that dimensions are allowed to form clusters. Each cluster of dimensions is then segmented separately. We formally define the problem of clustered segmentations and we experimentally show that segmenting sequences using this segmentation model, leads to solutions with smaller error for the same model cost. Segmentation with rearrangements is a novel variation to the segmentation problem: in addition to partitioning the sequence we also seek to apply a limited amount of reordering, so that the overall representation error is minimized. We formulate the problem of segmentation with rearrangements and we show that it is an NP-hard problem to solve or even to approximate. We devise effective algorithms for the proposed problem, combining ideas from dynamic programming and outlier detection algorithms in sequences. In the final part of the thesis, we discuss the problem of aggregating results of segmentation algorithms on the same set of data points. In this case, we are interested in producing a partitioning of the data that agrees as much as possible with the input partitions. We show that this problem can be solved optimally in polynomial time using dynamic programming. Furthermore, we show that not all data points are candidates for segment boundaries in the optimal solution.

Multi-user resource-sharing problem for the Internet

In this thesis we study a series of multi-user resource-sharing problems for the Internet, which involve distribution of a common resource among participants of multi-user systems (servers or networks). We study concurrently accessible resources, which for end-users may be exclusively accessible or non-exclusively. For all kinds we suggest a separate algorithm or a modification of common reputation scheme. Every algorithm or method is studied from different perspectives: optimality of protocols, selfishness of end users, fairness of the protocol for end users. On the one hand the multifaceted analysis allows us to select the most suited protocols among a set of various available ones based on trade-offs of optima criteria. On the other hand, the future Internet predictions dictate new rules for the optimality we should take into account and new properties of the networks that cannot be neglected anymore. In this thesis we have studied new protocols for such resource-sharing problems as the backoff protocol, defense mechanisms against Denial-of-Service, fairness and confidentiality for users in overlay networks. For backoff protocol we present analysis of a general backoff scheme, where an optimization is applied to a general-view backoff function. It leads to an optimality condition for backoff protocols in both slot times and continuous time models. Additionally we present an extension for the backoff scheme in order to achieve fairness for the participants in an unfair environment, such as wireless signal strengths. Finally, for the backoff algorithm we suggest a reputation scheme that deals with misbehaving nodes. For the next problem -- denial-of-service attacks, we suggest two schemes that deal with the malicious behavior for two conditions: forged identities and unspoofed identities. For the first one we suggest a novel most-knocked-first-served algorithm, while for the latter we apply a reputation mechanism in order to restrict resource access for misbehaving nodes. Finally, we study the reputation scheme for the overlays and peer-to-peer networks, where resource is not placed on a common station, but spread across the network. The theoretical analysis suggests what behavior will be selected by the end station under such a reputation mechanism.

Optimisation Problems in Wireless Sensor Networks : Local Algorithms and Local Graphs

This thesis studies optimisation problems related to modern large-scale distributed systems, such as wireless sensor networks and wireless ad-hoc networks. The concrete tasks that we use as motivating examples are the following: (i) maximising the lifetime of a battery-powered wireless sensor network, (ii) maximising the capacity of a wireless communication network, and (iii) minimising the number of sensors in a surveillance application. A sensor node consumes energy both when it is transmitting or forwarding data, and when it is performing measurements. Hence task (i), lifetime maximisation, can be approached from two different perspectives. First, we can seek for optimal data flows that make the most out of the energy resources available in the network; such optimisation problems are examples of so-called max-min linear programs. Second, we can conserve energy by putting redundant sensors into sleep mode; we arrive at the sleep scheduling problem, in which the objective is to find an optimal schedule that determines when each sensor node is asleep and when it is awake. In a wireless network simultaneous radio transmissions may interfere with each other. Task (ii), capacity maximisation, therefore gives rise to another scheduling problem, the activity scheduling problem, in which the objective is to find a minimum-length conflict-free schedule that satisfies the data transmission requirements of all wireless communication links. Task (iii), minimising the number of sensors, is related to the classical graph problem of finding a minimum dominating set. However, if we are not only interested in detecting an intruder but also locating the intruder, it is not sufficient to solve the dominating set problem; formulations such as minimum-size identifying codes and locating dominating codes are more appropriate. This thesis presents approximation algorithms for each of these optimisation problems, i.e., for max-min linear programs, sleep scheduling, activity scheduling, identifying codes, and locating dominating codes. Two complementary approaches are taken. The main focus is on local algorithms, which are constant-time distributed algorithms. The contributions include local approximation algorithms for max-min linear programs, sleep scheduling, and activity scheduling. In the case of max-min linear programs, tight upper and lower bounds are proved for the best possible approximation ratio that can be achieved by any local algorithm. The second approach is the study of centralised polynomial-time algorithms in local graphs these are geometric graphs whose structure exhibits spatial locality. Among other contributions, it is shown that while identifying codes and locating dominating codes are hard to approximate in general graphs, they admit a polynomial-time approximation scheme in local graphs.

Confronting Confucian Understandings of the Christian Doctrine of Salvation : A systematic theological analysis of the basic problems in the Confucian-Christian dialogue

The aim of the present study is to analyze Confucian understandings of the Christian doctrine of salvation in order to find the basic problems in the Confucian-Christian dialogue. I will approach the task via a systematic theological analysis of four issues in order to limit the thesis to an appropriate size. They are analyzed in three chapters as follows: 1. The Confucian concept concerning the existence of God. Here I discuss mainly the issue of assimilation of the Christian concept of God to the concepts of Sovereign on High (Shangdi) and Heaven (Tian) in Confucianism. 2. The Confucian understanding of the object of salvation and its status in Christianity. 3. The Confucian understanding of the means of salvation in Christianity. Before beginning this analysis it is necessary to clarify the vast variety of controversies, arguments, ideas, opinions and comments expressed in the name of Confucianism; thus, clear distinctions among different schools of Confucianism are given in chapter 2. In the last chapter I will discuss the results of my research in this study by pointing out the basic problems that will appear in the analysis. The results of the present study provide conclusions in three related areas: the tacit differences in the ways of thinking between Confucians and Christians, the basic problems of the Confucian-Christian dialogue, and the affirmative elements in the dialogue. In addition to a summary, a bibliography and an index, there are also eight appendices, where I have introduced important background information for readers to understand the present study.

Traditional Village Governance (Desa Adat) and Inter-ethnic Conflict in Bali : A Study of Conflict between Balinese and Migrants: Cases from Municipality of Denpasar

Regional autonomy in Indonesia was initially introduced as a means of pacifying regional disappointment at the central government. Not only did the Regional Autonomy Law of 1999 give the Balinese a chance to express grievance regarding the centralist policies of the Jakarta government but also provided an opportunity to return to the regional, exclusive, traditional village governance (desa adat). As a result, the problems faced by the island, particularly ethnic conflicts, are increasingly handled by the mechanism of this traditional type of governance. Traditional village governance with regard to ethnic conflicts (occurring) between Balinese and migrants has never been systematically analyzed. Existing analyses emphasized only the social context, but do not explain either the cause of conflicts and the ensuing problems entails or the virtues of traditional village governance mechanisms for mediating in the conflict. While some accounts provide snapshots, they lack both theoretical and conflict study perspective. The primary aim of this dissertation is to explore the expression and the causes of conflict between the Balinese and migrants and to advance the potential of traditional village governance as a means of conflict resolution with particular reference to the municipality of Denpasar. One conclusion of the study is that the conflict between the Balinese and migrants has been expressed on the level of situation/contradiction, attitudes, and behavior. Yet the driving forces behind the conflict itself consist of the following factors: absence of cooperation; incompatible position and perception; inability to communicate effectively; and problem of inequality and injustice, which comes to the surface as a social, cultural, and economic problem. This complex of factors fuels collective fear for the future of both groups. The study concludes that traditional village governance mechanisms as a means of conflict resolution have not yet been able to provide an enduring resolution for the conflict. Analysis shows that the practice of traditional village governance is unable to provide satisfactory mechanisms for the conflict as prescribed by conflict resolution theory. Traditional village governance, which is derived from the exclusive Hindu-Balinese culture, is accepted as more legitimate among the Balinese than the official governance policies. However, it is not generally accepted by most of the Muslim migrants. In addition, traditional village governance lacks access to economic instruments, which weakens its capacity to tackle the economic roots of the conflict. Thus the traditional mechanisms of migrant ordinance , as practiced by the traditional village governance have not yet been successful in penetrating all aspects of the conflict. Finally, one of the main challenges for traditional village governance s legal development is the creation of a regional legal system capable of accommodating rapid changes in line with the national and international legal practices. The framing of the new laws should be responsive to the aspirations of a changing society. It should not only protect the various Balinese communities interests, but also that of other ethnic groups, especially those of the minority. In other words, the main challenge to traditional village governance is its ability to develop flexibility and inclusiveness.

Glutamatergic Modulation of Cue-Induced Drug-Seeking Behavior in the Rat

The characteristics of drug addiction include compulsive drug use despite negative consequences and re-occurring relapses, returns to drug use after a period of abstinence. Therefore, relapse prevention is one of the major challenges for the treatment of drug addiction. There are three main factors capable of inducing craving for drugs and triggering relapse long after cessation of drug use and dissipation of physical withdrawal signs: stress, re-exposure to the drug, and environmental stimuli (cues) that have been previously associated with drug use. The neurotransmitters dopamine and glutamate have been implicated in the modulation of drug-seeking behavior. The aim of this project was to examine the role of glutamatergic neurotransmission in relapse triggered by conditioned drug-associated stimuli. The focus was on clarifying whether relapse to drug seeking can be attenuated by blockade of glutamate receptors. In addition, as the nucleus accumbens has been proposed to participate in the modulation of drug-seeking behavior, the effects of glutamate receptor blockade in this brain structure on cue-induced relapse were investigated. The studies employed animals models in which rats were trained to press a lever in a test cage to obtain alcohol or intravenous cocaine. Drug availability was paired with distinct olfactory, auditory, or visual stimuli. This phase was followed by extinction training, during which lever presses did not result in the presentation of the drug or the drug-associated stimuli. Extinction training led to a gradual decrease in the number of lever presses during test sessions. Relapse was triggered by presenting the rats with the drug-associated stimuli in the absence of alcohol or cocaine. The drug-associated stimuli were alone capable of inducing resumption of lever pressing and maintaining this behavior during repeated testing. The number of lever presses during a session represented the intensity of drug-seeking and relapse behavior. The results suggest that glutamatergic neurotransmission is involved in the modulation of drug-seeking behavior. Both alcohol and cocaine relapse were attenuated by systemic pretreatment with glutamate receptor antagonists. However, differences were found in the ability of ionotropic AMPA/kainate and NMDA receptor antagonists to regulate drug-seeking behavior. The AMPA/kainate antagonists CNQX and NBQX, and L-701,324, an antagonist with affinity for the glycine site of the NMDA receptor, attenuated cue-induced drug seeking, whereas the competitive NMDA antagonist CGP39551 and the NMDA channel blocker MK-801 were without effect. MPEP, an antagonist at metabotropic mGlu5 glutamate receptors, also decreased drug seeking, but its administration was found to lead to conditioned suppression of behavior during subsequent treatment sessions, suggesting that MPEP may have undesirable side effects. The mGluR2/3 agonist LY379268 and the mGluR8 agonist (S)-3,4-DCPG decreased both cue-induced relapse to alcohol drinking and alcohol consumption. Control experiments showed however that administration of the agonists was accompanied by motor suppression limiting their usefulness. Administration of the AMPA/kainate antagonist CNQX, the NMDA antagonist D-AP5, and the mGluR5 antagonist MPEP into the nucleus accumbens resulted also in a decrease in drug-seeking behavior, suggesting that the nucleus accumbens is at least one of the anatomical sites regulating drug seeking and mediating the effects of glutamate receptor antagonists on this behavior.

Juvenile neuronal ceroid lipofuscinosis; psychiatric symptoms, GAD-autoantibodies, and response to medication

Juvenile neuronal ceroid lipofuscinosis (JNCL) is one of the most common neurodegenerative diseases in childhood. Its clinical onset, with visual failure as the first sign, is between the ages of 4 to 8 years. During the disease progress, epilepsy, motor symptoms, cognitive decline, and psychiatric symptoms become apparent. It leads to premature death between ages 15 and 30. Treatment consists of symptomatic drug administration and various forms of rehabilitation, but to date, no curative treatment exists. To gain a more comprehensive picture of psychiatric problems, symptoms were evaluated by the Child Behavior Checklist, the Teacher Report Form, and the Children s Depression Inventory. The JNCL patients had a great number of severe psychiatric symptoms, with wide inter-individual variability. The most common symptoms were social, thought, attention, and sleep problems, somatic complaints, and aggressive behaviour. Patients with psychotropic treatment had more problems than did those without psychotropic treatment, and female patients had more problems than did males. Between 10 and 20% of the patients reported depressive symptoms. In a 5-year follow-up, [123I]β-CIT SPECT and MRI revealed a tendency of decreasing serotonin transporter (SERT) availability and progressive brain atrophy. The correlation between changes in midbrain SERT and total brain volume was positive; no correlation appeared between SERT or brain atrophy and depressive symptoms. Thus, it seems likely that the low SERT availability is associated with progressive brain atrophy; it may also predispose towards depression, however. An open survey of psychotropic drugs and their efficacy was performed on JNCL patients in Finland. The most commonly used psychotropic drugs were the antidepressant citalopram and the antipsychotic risperidone. Their efficacy was good or satisfactory in the majority of cases and they seemed well tolerated. Quetiapine had a marked effect on one patient with a history of severe psychotic symptoms. Glutamate decarboxylase 65 autoantibodies (GAD65ab), found in JNCL patients, indicate that an immunomediated reaction against GAD or GABAergic neurons may play a part in the underlying pathogenetic mechanism. GAD65ab s also appeared in the serum of all eight JNCL patients included and intermittent corticosteroid therapy was initiated in all cases. After one year, the GAD65ab s had disappeared in the two oldest patients, who experienced an improvement in motor symptoms and alertness associated with their prednisolone therapy. Two younger patients experienced a significant IQ increase, but no change in GADab s. A randomized study with longer follow-up time is needed, however, to clarify the effect of prednisolone on disease progression.

Specific language impairment in pre-adolescence, adolescence, and adulthood with special emphasis on health-related quality of life

This clinical study focused on effects of childhood specific language impairment (SLI) on daily functioning in late life. SLI is a neurobiological disorder with genetic predisposition and manifests as poor language production or comprehension or both in a child with age-level non-verbal intelligence and no other known cause for deficient language development. The prevalence rate of around 7% puts it among the most prevalent developmental disorders in childhood. Negative long-term effects, such as problems in learning and behavior, are frequent. In follow-up studies the focus has seldom been on self-perception of daily functioning and participation, which are considered important in the International Classification of Functioning, Disability, and Health (ICF). To investigate the self-perceived aspects of everyday functioning in individuals with childhood receptive SLI compared with age- and gender-matched control populations, the 15D, 16D, and 17D health-related quality of life (HRQoL) questionnaires were applied. These generic questionnaires include 15, 16, and 17 dimensions, respectively, and give both a single index score and a profile with values on each dimension. Information on different life domains (rehabilitation, education, employment etc.) from each age-group was collected with separate questionnaires. The study groups comprised adults, adolescents (12-16 years), and pre-adolescents (8-11 years) who had received a diagnosis of receptive SLI and had been examined, usually before school age, at the Department of Phoniatrics of Helsinki University Central Hospital, where children with language deficits caused by various etiologies are examined and treated by a multidisciplinary team. The adult respondents included 33 subjects with a mean age of 34 years. Measured with 15D, the subjects perceived their HRQoL to be nearly as good as that of their controls, but on the dimensions of speech, usual activities, mental functioning, and distress they were significantly worse off. They significantly more often lived with their parents (19%) or were pensioned (26%) than the adult Finnish population on average. Adults with self-perceived problems in finding words and in remembering instructions, manifestations of persistent language impairment, showed inferior every day functioning to the rest of the study group. Of the adolescents and pre-adolescents, 48 and 51, respectively, responded. The majority in both groups had received special education or extra educational support at school. They all had attended speech therapy at some point; at the time of the study only one adolescent, but every third pre-adolescent still received speech therapy. The 16D score of the adolescent or the 17D score of the pre-adolescents did not differ from that of their controls. The 16D profiles differed on some dimensions; subjects were significantly worse off on the dimension of mental functioning, but better off on the dimension of vitality than controls. Of the 17D dimensions, the study group was significantly worse off on speech, whereas the control group reported significantly more problems in sleeping. Of the childhood performance measures investigated, low verbal intelligence quotient (VIQ), which is often considered to reflect receptive language impairment, was in adults subjects significantly associated with some of the self-perceived problems, such as problems in usual activities and mental functioning. The 15D, 16D, and 17D questionnaires served well in measuring self-perceived HRQoL. Such standardized measures with population values are especially important in confirming with the ICF guidelines. In the future these questionnaires could perhaps be used on a more individual level in follow-up of children in clinics, and even in special schools and classes, to detect those children at greatest risk of negative long-term effects and perhaps diminished well-being regarding daily functioning and participation.