Essays on Risk Modeling. Applications to Portfolio and Risk Management (summary section only)

In this thesis we deal with the concept of risk. The objective is to bring together and conclude on some normative information regarding quantitative portfolio management and risk assessment. The first essay concentrates on return dependency. We propose an algorithm for classifying markets into rising and falling. Given the algorithm, we derive a statistic: the Trend Switch Probability, for detection of long-term return dependency in the first moment. The empirical results suggest that the Trend Switch Probability is robust over various volatility specifications. The serial dependency in bear and bull markets behaves however differently. It is strongly positive in rising market whereas in bear markets it is closer to a random walk. Realized volatility, a technique for estimating volatility from high frequency data, is investigated in essays two and three. In the second essay we find, when measuring realized variance on a set of German stocks, that the second moment dependency structure is highly unstable and changes randomly. Results also suggest that volatility is non-stationary from time to time. In the third essay we examine the impact from market microstructure on the error between estimated realized volatility and the volatility of the underlying process. With simulation-based techniques we show that autocorrelation in returns leads to biased variance estimates and that lower sampling frequency and non-constant volatility increases the error variation between the estimated variance and the variance of the underlying process. From these essays we can conclude that volatility is not easily estimated, even from high frequency data. It is neither very well behaved in terms of stability nor dependency over time. Based on these observations, we would recommend the use of simple, transparent methods that are likely to be more robust over differing volatility regimes than models with a complex parameter universe. In analyzing long-term return dependency in the first moment we find that the Trend Switch Probability is a robust estimator. This is an interesting area for further research, with important implications for active asset allocation.

Feature integration in human vision

The earliest stages of human cortical visual processing can be conceived as extraction of local stimulus features. However, more complex visual functions, such as object recognition, require integration of multiple features. Recently, neural processes underlying feature integration in the visual system have been under intensive study. A specialized mid-level stage preceding the object recognition stage has been proposed to account for the processing of contours, surfaces and shapes as well as configuration. This thesis consists of four experimental, psychophysical studies on human visual feature integration. In two studies, classification image a recently developed psychophysical reverse correlation method was used. In this method visual noise is added to near-threshold stimuli. By investigating the relationship between random features in the noise and observer s perceptual decision in each trial, it is possible to estimate what features of the stimuli are critical for the task. The method allows visualizing the critical features that are used in a psychophysical task directly as a spatial correlation map, yielding an effective "behavioral receptive field". Visual context is known to modulate the perception of stimulus features. Some of these interactions are quite complex, and it is not known whether they reflect early or late stages of perceptual processing. The first study investigated the mechanisms of collinear facilitation, where nearby collinear Gabor flankers increase the detectability of a central Gabor. The behavioral receptive field of the mechanism mediating the detection of the central Gabor stimulus was measured by the classification image method. The results show that collinear flankers increase the extent of the behavioral receptive field for the central Gabor, in the direction of the flankers. The increased sensitivity at the ends of the receptive field suggests a low-level explanation for the facilitation. The second study investigated how visual features are integrated into percepts of surface brightness. A novel variant of the classification image method with brightness matching task was used. Many theories assume that perceived brightness is based on the analysis of luminance border features. Here, for the first time this assumption was directly tested. The classification images show that the perceived brightness of both an illusory Craik-O Brien-Cornsweet stimulus and a real uniform step stimulus depends solely on the border. Moreover, the spatial tuning of the features remains almost constant when the stimulus size is changed, suggesting that brightness perception is based on the output of a single spatial frequency channel. The third and fourth studies investigated global form integration in random-dot Glass patterns. In these patterns, a global form can be immediately perceived, if even a small proportion of random dots are paired to dipoles according to a geometrical rule. In the third study the discrimination of orientation structure in highly coherent concentric and Cartesian (straight) Glass patterns was measured. The results showed that the global form was more efficiently discriminated in concentric patterns. The fourth study investigated how form detectability depends on the global regularity of the Glass pattern. The local structure was either Cartesian or curved. It was shown that randomizing the local orientation deteriorated the performance only with the curved pattern. The results give support for the idea that curved and Cartesian patterns are processed in at least partially separate neural systems.

Integration of natural hazards, risk and climate change into spatial planning practices

Most countries of Europe, as well as many countries in other parts of the world, are experiencing an increased impact of natural hazards. It is often speculated, but not yet proven, that climate change might influence the frequency and magnitude of certain hydro-meteorological natural hazards. What has certainly been observed is a sharp increase in financial losses caused by natural hazards worldwide. Eventhough Europe appears to be a space that is not affected by natural hazards to such catastrophic extents as other parts of the world are, the damages experienced here are certainly increasing too. Natural hazards, climate change and, in particular, risks have therefore recently been put high on the political agenda of the EU. In the search for appropriate instruments for mitigating impacts of natural hazards and climate change, as well as risks, the integration of these factors into spatial planning practices is constantly receiving higher attention. The focus of most approaches lies on single hazards and climate change mitigation strategies. The current paradigm shift of climate change mitigation to adaptation is used as a basis to draw conclusions and recommendations on what concepts could be further incorporated into spatial planning practices. Especially multi-hazard approaches are discussed as an important approach that should be developed further. One focal point is the definition and applicability of the terms natural hazard, vulnerability and risk in spatial planning practices. Especially vulnerability and risk concepts are so many-fold and complicated that their application in spatial planning has to be analysed most carefully. The PhD thesis is based on six published articles that describe the results of European research projects, which have elaborated strategies and tools for integrated communication and assessment practices on natural hazards and climate change impacts. The papers describe approaches on local, regional and European level, both from theoretical and practical perspectives. Based on these, passed, current and future potential spatial planning applications are reviewed and discussed. In conclusion it is recommended to shift from single hazard assessments to multi-hazard approaches, integrating potential climate change impacts. Vulnerability concepts should play a stronger role than present, and adaptation to natural hazards and climate change should be more emphasized in relation to mitigation. It is outlined that the integration of risk concepts in planning is rather complicated and would need very careful assessment to ensure applicability. Future spatial planning practices should also consider to be more interdisciplinary, i.e. to integrate as many stakeholders and experts as possible to ensure the sustainability of investments.

Composition operators on vector-valued BMOA and related function spaces

A composition operator is a linear operator between spaces of analytic or harmonic functions on the unit disk, which precomposes a function with a fixed self-map of the disk. A fundamental problem is to relate properties of a composition operator to the function-theoretic properties of the self-map. During the recent decades these operators have been very actively studied in connection with various function spaces. The study of composition operators lies in the intersection of two central fields of mathematical analysis; function theory and operator theory. This thesis consists of four research articles and an overview. In the first three articles the weak compactness of composition operators is studied on certain vector-valued function spaces. A vector-valued function takes its values in some complex Banach space. In the first and third article sufficient conditions are given for a composition operator to be weakly compact on different versions of vector-valued BMOA spaces. In the second article characterizations are given for the weak compactness of a composition operator on harmonic Hardy spaces and spaces of Cauchy transforms, provided the functions take values in a reflexive Banach space. Composition operators are also considered on certain weak versions of the above function spaces. In addition, the relationship of different vector-valued function spaces is analyzed. In the fourth article weighted composition operators are studied on the scalar-valued BMOA space and its subspace VMOA. A weighted composition operator is obtained by first applying a composition operator and then a pointwise multiplier. A complete characterization is given for the boundedness and compactness of a weighted composition operator on BMOA and VMOA. Moreover, the essential norm of a weighted composition operator on VMOA is estimated. These results generalize many previously known results about composition operators and pointwise multipliers on these spaces.

Inverse Problem for Fractional Brownian Motion with Discrete Data

The problem of recovering information from measurement data has already been studied for a long time. In the beginning, the methods were mostly empirical, but already towards the end of the sixties Backus and Gilbert started the development of mathematical methods for the interpretation of geophysical data. The problem of recovering information about a physical phenomenon from measurement data is an inverse problem. Throughout this work, the statistical inversion method is used to obtain a solution. Assuming that the measurement vector is a realization of fractional Brownian motion, the goal is to retrieve the amplitude and the Hurst parameter. We prove that under some conditions, the solution of the discretized problem coincides with the solution of the corresponding continuous problem as the number of observations tends to infinity. The measurement data is usually noisy, and we assume the data to be the sum of two vectors: the trend and the noise. Both vectors are supposed to be realizations of fractional Brownian motions, and the goal is to retrieve their parameters using the statistical inversion method. We prove a partial uniqueness of the solution. Moreover, with the support of numerical simulations, we show that in certain cases the solution is reliable and the reconstruction of the trend vector is quite accurate.

Boundedness of weakly singular integral operators on domains

The monograph dissertation deals with kernel integral operators and their mapping properties on Euclidean domains. The associated kernels are weakly singular and examples of such are given by Green functions of certain elliptic partial differential equations. It is well known that mapping properties of the corresponding Green operators can be used to deduce a priori estimates for the solutions of these equations. In the dissertation, natural size- and cancellation conditions are quantified for kernels defined in domains. These kernels induce integral operators which are then composed with any partial differential operator of prescribed order, depending on the size of the kernel. The main object of study in this dissertation being the boundedness properties of such compositions, the main result is the characterization of their Lp-boundedness on suitably regular domains. In case the aforementioned kernels are defined in the whole Euclidean space, their partial derivatives of prescribed order turn out to be so called standard kernels that arise in connection with singular integral operators. The Lp-boundedness of singular integrals is characterized by the T1 theorem, which is originally due to David and Journé and was published in 1984 (Ann. of Math. 120). The main result in the dissertation can be interpreted as a T1 theorem for weakly singular integral operators. The dissertation deals also with special convolution type weakly singular integral operators that are defined on Euclidean spaces.

Composition operators, Aleksandrov measures and value distribution of analytic maps in the unit disc

A composition operator is a linear operator that precomposes any given function with another function, which is held fixed and called the symbol of the composition operator. This dissertation studies such operators and questions related to their theory in the case when the functions to be composed are analytic in the unit disc of the complex plane. Thus the subject of the dissertation lies at the intersection of analytic function theory and operator theory. The work contains three research articles. The first article is concerned with the value distribution of analytic functions. In the literature there are two different conditions which characterize when a composition operator is compact on the Hardy spaces of the unit disc. One condition is in terms of the classical Nevanlinna counting function, defined inside the disc, and the other condition involves a family of certain measures called the Aleksandrov (or Clark) measures and supported on the boundary of the disc. The article explains the connection between these two approaches from a function-theoretic point of view. It is shown that the Aleksandrov measures can be interpreted as kinds of boundary limits of the Nevanlinna counting function as one approaches the boundary from within the disc. The other two articles investigate the compactness properties of the difference of two composition operators, which is beneficial for understanding the structure of the set of all composition operators. The second article considers this question on the Hardy and related spaces of the disc, and employs Aleksandrov measures as its main tool. The results obtained generalize those existing for the case of a single composition operator. However, there are some peculiarities which do not occur in the theory of a single operator. The third article studies the compactness of the difference operator on the Bloch and Lipschitz spaces, improving and extending results given in the previous literature. Moreover, in this connection one obtains a general result which characterizes the compactness and weak compactness of the difference of two weighted composition operators on certain weighted Hardy-type spaces.

NORDEK : A Plan for Increased Nordic Economic Co-operation and Integration 1968-1970

For the first time the attempt of Denmark, Finland, Norway and Sweden to increase Nordic economic co-operation and integration (NORDEK 1968-1970) is analysed by using records from the four governments archives and interviews with central actors participating. A dominating argument has until now been that dynamics in Nordic economic integration is different from dynamics in European integration. This archive based study disproves the myth however of ideological Nordism and of short term political developments outside Norden as most important for the NORDEK initiative. The NORDEK initiative was actually more a consequence of a long term socioeconomic and socio-political path dependant process. The study also disproves the myth that the NORDEK plan was a political and ideological symbol without socioeconomic substance. The purpose with NORDEK was to create a better basis for generating economic growth and social welfare. The proposed NORDEK institutions were therefore developed to promote economic progress. The study finally shows that the NORDEK failure in 1970 was not a result of lacking economic rationale or incompatible economic interests. The failure was a result of a power struggle in Finnish domestic policy and lacking political will in the other Nordic countries to continue without Finland.

Regional Integration and the State : The Changing Nature of Sovereignty in Southern Africa and Europe

The study explores the role of the state in regional integration processes. The question is approached through theoretical discussion and two case-studies - SADC (Southern African Development Community) and the EU. The main research question of the study is, what are the possibilities and problems of the integration process in Southern Africa and how do they differ from the possibilities and problems of the integration process in Europe. The undelrying question of the study is why do states decide to participate in an integration process where they have to limit their sovereignty. Review of the theoretical discussion of the integration studies shows that the integration process is affected by several factors on different levels of the international system. But the state plays a central role in integration processes - integration processes are inititated and carried on by the participatig states. The European integration process shows that the interests of the state can change over time. At the beginning of the integration process, the objective was to strengthen participating states. Later EU member states have decided that it is in their interest to deepen the process even if it has meant limitation of their sovereignty. The determinant factor has been that the member states have considered it to be in their interst to deepen the process. In Southern Africa the integration process is only at the beginning. SADC aims to establish a free trade area by 2008. The biggest challenge is how to implement the integration process so that it benefits all member states in a region that is economically dominated by South Africa. In practice this can be achieved through establishment of corrective mechanisms, which ensure equitable distribution of benefits. This would require deeper integration and South Africa to adapt responsibility towards its regional partners. African integration processes in general have not been as successful as for example the EU. African states have been reluctant to limit their sovereignty in favour of regional organisations.This can be explained by the differences between European and African states. The EU member states have been democracies while African states have been characterised by concentration of power in the executive branch. Furthermore the political systems in Africa have been characterised by vertical clientelist reltionships. As a result it has not been in the interest of the political elite to limit the state sovereignty in favour of regional organisations. In recent years SADC has been relatively succesful in its integration process and reforms, but a lot remains to be done before the implementation of the free trade area can be succesful. The institutional structure and treaties of SADC differ from the structures of the EU. Member states are the main actors of the integration processes. Their differences are reflected in the process and produce different kinds of integration in different parts of the world.