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.

Society by Numbers : Studies on Model-Based Explanations in the Social Sciences

The aim of this dissertation is to provide conceptual tools for the social scientist for clarifying, evaluating and comparing explanations of social phenomena based on formal mathematical models. The focus is on relatively simple theoretical models and simulations, not statistical models. These studies apply a theory of explanation according to which explanation is about tracing objective relations of dependence, knowledge of which enables answers to contrastive why and how-questions. This theory is developed further by delineating criteria for evaluating competing explanations and by applying the theory to social scientific modelling practices and to the key concepts of equilibrium and mechanism. The dissertation is comprised of an introductory essay and six published original research articles. The main theses about model-based explanations in the social sciences argued for in the articles are the following. 1) The concept of explanatory power, often used to argue for the superiority of one explanation over another, compasses five dimensions which are partially independent and involve some systematic trade-offs. 2) All equilibrium explanations do not causally explain the obtaining of the end equilibrium state with the multiple possible initial states. Instead, they often constitutively explain the macro property of the system with the micro properties of the parts (together with their organization). 3) There is an important ambivalence in the concept mechanism used in many model-based explanations and this difference corresponds to a difference between two alternative research heuristics. 4) Whether unrealistic assumptions in a model (such as a rational choice model) are detrimental to an explanation provided by the model depends on whether the representation of the explanatory dependency in the model is itself dependent on the particular unrealistic assumptions. Thus evaluating whether a literally false assumption in a model is problematic requires specifying exactly what is supposed to be explained and by what. 5) The question of whether an explanatory relationship depends on particular false assumptions can be explored with the process of derivational robustness analysis and the importance of robustness analysis accounts for some of the puzzling features of the tradition of model-building in economics. 6) The fact that economists have been relatively reluctant to use true agent-based simulations to formulate explanations can partially be explained by the specific ideal of scientific understanding implicit in the practise of orthodox economics.

From Iron Horse to Rauta-airot - a Semiotic View on the Domestication of Metaphors in Literary Translation

The thesis concentrates on two questions: the translation of metaphors in literary texts, and the use of semiotic models and tools in translation studies. The aim of the thesis is to present a semiotic, text based model designed to ease the translation of metaphors and to analyze translated metaphors. In the translation of metaphors I will concentrate on the central problem of metaphor translations: in addition to its denotation and connotation, a single metaphor may contain numerous culture or genre specific meanings. How can a translator ensure the translation of all meanings relevant to the text as a whole? I will approach the question from two directions. Umberto Eco's holistic text analysis model provides an opportunity to concentrate on the problematic nature of metaphor translation from the level of a text as a specific entity, while George Lakoff's and Mark Johnson's metaphor research makes it possible to approach the question from the level of individual metaphors. On the semiotic side, the model utilizes Eero Tarasti's existential semiotics supported by Algirdas Greimas' actant model and Yuri Lotman's theory of cultural semiotics. In the model introduced in the thesis, individual texts are deconstructed through Eco's model into elements. The textual roles and features of these elements are distilled further through Tarasti's model into their coexistent meaning levels. The priorization and analysis of these meaning levels provide an opportunity to consider the contents and significance of specific metaphors in relation to the needs of the text as a whole. As example texts, I will use Motörhead's hard rock classic Iron Horse/Born to Lose and its translation into Rauta-airot by Viikate. I will use the introduced model to analyze the metaphors in the source and target texts, and to consider the transfer of culture specific elements between the languages and cultural borders. In addition, I will use the analysis process to examine the validity of the model introduced in the thesis.

Mechanism of RNA Translocation by a Viral Packaging Motor

Molecular motors are proteins that convert chemical energy into mechanical work. The viral packaging ATPase P4 is a hexameric molecular motor that translocates RNA into preformed viral capsids. P4 belongs to the ubiquitous class of hexameric helicases. Although its structure is known, the mechanism of RNA translocation remains elusive. Here we present a detailed kinetic study of nucleotide binding, hydrolysis, and product release by P4. We propose a stochastic-sequential cooperative model to describe the coordination of ATP hydrolysis within the hexamer. In this model the apparent cooperativity is a result of hydrolysis stimulation by ATP and RNA binding to neighboring subunits rather than cooperative nucleotide binding. Simultaneous interaction of neighboring subunits with RNA makes the otherwise random hydrolysis sequential and processive. Further, we use hydrogen/deuterium exchange detected by high resolution mass spectrometry to visualize P4 conformational dynamics during the catalytic cycle. Concerted changes of exchange kinetics reveal a cooperative unit that dynamically links ATP binding sites and the central RNA binding channel. The cooperative unit is compatible with the structure-based model in which translocation is effected by conformational changes of a limited protein region. Deuterium labeling also discloses the transition state associated with RNA loading which proceeds via opening of the hexameric ring. Hydrogen/deuterium exchange is further used to delineate the interactions of the P4 hexamer with the viral procapsid. P4 associates with the procapsid via its C-terminal face. The interactions stabilize subunit interfaces within the hexamer. The conformation of the virus-bound hexamer is more stable than the hexamer in solution, which is prone to spontaneous ring openings. We propose that the stabilization within the viral capsid increases the packaging processivity and confers selectivity during RNA loading. Finally, we use single molecule techniques to characterize P4 translocation along RNA. While the P4 hexamer encloses RNA topologically within the central channel, it diffuses randomly along the RNA. In the presence of ATP, unidirectional net movement is discernible in addition to the stochastic motion. The diffusion is hindered by activation energy barriers that depend on the nucleotide binding state. The results suggest that P4 employs an electrostatic clutch instead of cycling through stable, discrete, RNA binding states during translocation. Conformational changes coupled to ATP hydrolysis modify the electrostatic potential inside the central channel, which in turn biases RNA motion in one direction. Implications of the P4 model for other hexameric molecular motors are discussed.

Generalised regression estimation for domain class frequencies

This study examines the properties of Generalised Regression (GREG) estimators for domain class frequencies and proportions. The family of GREG estimators forms the class of design-based model-assisted estimators. All GREG estimators utilise auxiliary information via modelling. The classic GREG estimator with a linear fixed effects assisting model (GREG-lin) is one example. But when estimating class frequencies, the study variable is binary or polytomous. Therefore logistic-type assisting models (e.g. logistic or probit model) should be preferred over the linear one. However, other GREG estimators than GREG-lin are rarely used, and knowledge about their properties is limited. This study examines the properties of L-GREG estimators, which are GREG estimators with fixed-effects logistic-type models. Three research questions are addressed. First, I study whether and when L-GREG estimators are more accurate than GREG-lin. Theoretical results and Monte Carlo experiments which cover both equal and unequal probability sampling designs and a wide variety of model formulations show that in standard situations, the difference between L-GREG and GREG-lin is small. But in the case of a strong assisting model, two interesting situations arise: if the domain sample size is reasonably large, L-GREG is more accurate than GREG-lin, and if the domain sample size is very small, estimation of assisting model parameters may be inaccurate, resulting in bias for L-GREG. Second, I study variance estimation for the L-GREG estimators. The standard variance estimator (S) for all GREG estimators resembles the Sen-Yates-Grundy variance estimator, but it is a double sum of prediction errors, not of the observed values of the study variable. Monte Carlo experiments show that S underestimates the variance of L-GREG especially if the domain sample size is minor, or if the assisting model is strong. Third, since the standard variance estimator S often fails for the L-GREG estimators, I propose a new augmented variance estimator (A). The difference between S and the new estimator A is that the latter takes into account the difference between the sample fit model and the census fit model. In Monte Carlo experiments, the new estimator A outperformed the standard estimator S in terms of bias, root mean square error and coverage rate. Thus the new estimator provides a good alternative to the standard estimator.

Detecting Earnings Management Using Neural Networks

Detecting Earnings Management Using Neural Networks. Trying to balance between relevant and reliable accounting data, generally accepted accounting principles (GAAP) allow, to some extent, the company management to use their judgment and to make subjective assessments when preparing financial statements. The opportunistic use of the discretion in financial reporting is called earnings management. There have been a considerable number of suggestions of methods for detecting accrual based earnings management. A majority of these methods are based on linear regression. The problem with using linear regression is that a linear relationship between the dependent variable and the independent variables must be assumed. However, previous research has shown that the relationship between accruals and some of the explanatory variables, such as company performance, is non-linear. An alternative to linear regression, which can handle non-linear relationships, is neural networks. The type of neural network used in this study is the feed-forward back-propagation neural network. Three neural network-based models are compared with four commonly used linear regression-based earnings management detection models. All seven models are based on the earnings management detection model presented by Jones (1991). The performance of the models is assessed in three steps. First, a random data set of companies is used. Second, the discretionary accruals from the random data set are ranked according to six different variables. The discretionary accruals in the highest and lowest quartiles for these six variables are then compared. Third, a data set containing simulated earnings management is used. Both expense and revenue manipulation ranging between -5% and 5% of lagged total assets is simulated. Furthermore, two neural network-based models and two linear regression-based models are used with a data set containing financial statement data from 110 failed companies. Overall, the results show that the linear regression-based models, except for the model using a piecewise linear approach, produce biased estimates of discretionary accruals. The neural network-based model with the original Jones model variables and the neural network-based model augmented with ROA as an independent variable, however, perform well in all three steps. Especially in the second step, where the highest and lowest quartiles of ranked discretionary accruals are examined, the neural network-based model augmented with ROA as an independent variable outperforms the other models.