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This dissertation examines the relevance of regimes for stock markets. In three research articles, we cover the identification and predictability of regimes and their relationships to macroeconomic and financial variables in the United States.
The initial two chapters contribute to the debate on the predictability of stock markets. While various approaches can demonstrate in-sample predictability, their predictive power diminishes substantially in out-of-sample studies. Parameter instability and model uncertainty are the primary challenges. However, certain methods have demonstrated efficacy in addressing these issues. In Chapter 1 and 2, we present frameworks that combine these methods meaningfully. Chapter 3 focuses on the role of regimes in explaining macro-financial relationships and examines the state-dependent effects of macroeconomic expectations on cross-sectional stock returns. Although it is common to capture the variation in stock returns using factor models, their macroeconomic risk sources are unclear. According to macro-financial asset pricing, expectations about state variables may be viable candidates to explain these sources. We examine their usefulness in explaining factor premia and assess their suitability for pricing stock portfolios.
In summary, this dissertation improves our understanding of stock market regimes in three ways. First, we show that it is worthwhile to exploit the regime dependence of stock markets. Markov-switching models and their extensions are valuable tools for filtering the stock market dynamics and identifying and predicting regimes in real-time. Moreover, accounting for regime-dependent relationships helps to examine the dynamic impact of macroeconomic shocks on stock returns. Second, we emphasize the usefulness of macro-financial variables for the stock market. Regime identification and forecasting benefit from their inclusion. This is particularly true in periods of high uncertainty when information processing in financial markets is less efficient. Finally, we recommend to address parameter instability, estimation risk, and model uncertainty in empirical models. Because it is difficult to find a single approach that meets all of these challenges simultaneously, it is advisable to combine appropriate methods in a meaningful way. The framework should be as complex as necessary but as parsimonious as possible to mitigate additional estimation risk. This is especially recommended when working with financial market data with a typically low signal-to-noise ratio.
Mixed-Integer Optimization Techniques for Robust Bilevel Problems with Here-and-Now Followers
(2025)
In bilevel optimization, some of the variables of an optimization problem have to be an optimal solution to another nested optimization problem. This specific structure renders bilevel optimization a powerful tool for modeling hierarchical decision-making processes, which arise in various real-world applications such as in critical infrastructure defense, transportation, or energy. Due to their nested structure, however, bilevel problems are also inherently hard to solve—both in theory and in practice. Further challenges arise if, e.g., bilevel problems under uncertainty are considered.
In this dissertation, we address different types of uncertainties in bilevel optimization using techniques from robust optimization. We study mixed-integer linear bilevel problems with lower-level objective uncertainty, which we tackle using the notion of Gamma-robustness. We present two exact branch-and-cut approaches to solve these Gamma-robust bilevel problems, along with cuts tailored to the important class of monotone interdiction problems. Given the overall hardness of the considered problems, we additionally propose heuristic approaches for mixed-integer, linear, and Gamma-robust bilevel problems. The latter rely on solving a linear number of deterministic bilevel problems so that no problem-specific tailoring is required. We assess the performance of both the exact and the heuristic approaches through extensive computational studies.
In addition, we study the problem of determining optimal tolls in a traffic network in which the network users hedge against uncertain travel costs in a robust way. The overall toll-setting problem can be seen as a single-leader multi-follower problem with multiple robustified followers. We model this setting as a mathematical problem with equilibrium constraints, for which we present a mixed-integer, nonlinear, and nonconvex reformulation that can be tackled using state-of-the-art general-purpose solvers. We further illustrate the impact of considering robustified followers on the toll-setting policies through a case study.
Finally, we highlight that the sources of uncertainty in bilevel optimization are much richer compared to single-level optimization. To this end, we study two aspects related to so-called decision uncertainty. First, we propose a strictly robust approach in which the follower hedges against erroneous observations of the leader's decision. Second, we consider an exemplary bilevel problem with a continuous but nonconvex lower level in which algorithmic necessities prevent the follower from making a globally optimal decision in an exact sense. The example illustrates that even very small deviations in the follower's decision may lead to arbitrarily large discrepancies between exact and computationally obtained bilevel solutions.
Partial differential equations are not always suited to model all physical phenomena, especially, if long-range interactions are involved or if the actual solution might not satisfy the regularity requirements associated with the partial differential equation. One remedy to this problem are nonlocal operators, which typically consist of integrals that incorporate interactions between two separated points in space and the corresponding solutions to nonlocal equations have to satisfy less regularity conditions.
In PDE-constrained shape optimization the goal is to minimize or maximize an objective functional that is dependent on the shape of a certain domain and on the solution to a partial differential equation, which is usually also influenced by the shape of this domain. Moreover, parameters associated with the nonlocal model are oftentimes domain dependent and thus it is a natural next step to now consider shape optimization problems that are governed by nonlocal equations.
Therefore, an interface identification problem constrained by nonlocal equations is thoroughly investigated in this thesis. Here, we focus on rigorously developing the first and second shape derivative of the associated reduced functional. In addition, we study first- and second-order shape optimization algorithms in multiple numerical experiments.
Moreover, we also propose Schwarz methods for nonlocal Dirichlet problems as well as regularized nonlocal Neumann problems. Particularly, we investigate the convergence of the multiplicative Schwarz approach and we conduct a number of numerical experiments, which illustrate various aspects of the Schwarz method applied to nonlocal equations.
Since applying the finite element method to solve nonlocal problems numerically can be quite costly, Local-to-Nonlocal couplings emerged, which combine the accuracy of nonlocal models on one part of the domain with the fast computation of partial differential equations on the remaining area. Therefore, we also examine the interface identification problem governed by an energy-based Local-to-Nonlocal coupling, which can be numerically computed by making use of the Schwarz method. Here, we again present a formula for the shape derivative of the associated reduced functional and investigate a gradient based shape optimization method.
In machine learning, classification is the task of predicting a label for each point within a data set. When the class of each point in the labeled subset is already known, this information is used to recognize patterns and make predictions about the points in the remainder of the set, referred to as the unlabeled set. This scenario falls in the field of supervised learning.
However, the number of labeled points can be restricted, because, e.g., it is expensive to obtain this information. Besides, this subset may be biased, such as in the case of self-selection in a survey. Consequently, the classification performance for unlabeled points may be limited. To improve the reliability of the results, semi-supervised learning tackles the setting of labeled and unlabeled data. Moreover, in many cases, additional information about the size of each class can be available from undisclosed sources.
This cumulative thesis presents different studies to combine this external cardinality constraint information within three important algorithms for binary classification in the supervised context: support vector machines (SVM), classification trees, and random forests. From a mathematical point of view, we focus on mixed-integer programming (MIP) models for semi-supervised approaches that consider a cardinality constraint for each class for each algorithm.
Furthermore, since the proposed MIP models are computationally challenging, we also present techniques that simplify the process of solving these problems. In the SVM setting, we introduce a re-clustering method and further computational techniques to reduce the computational cost. In the context of classification trees, we provide correct values for certain bounds that play a crucial role for the solver performance. For the random forest model, we develop preprocessing techniques and an intuitive branching rule to reduce the solution time. For all three methods, our numerical results show that our approaches have better statistical performances for biased samples than the standard approach.
Optimal Error Bounds in Normal and Edgeworth Approximation of Symmetric Binomial and Related Laws
(2024)
This thesis explores local and global normal and Edgeworth approximations for symmetric
binomial distributions. Further, it examines the normal approximation of convolution powers
of continuous and discrete uniform distributions.
We obtain the optimal constant in the local central limit theorem for symmetric binomial
distributions and its analogs in higher-order Edgeworth approximation. Further, we offer a
novel proof for the known optimal constant in the global central limit theorem for symmetric
binomial distributions using Fourier inversion. We also consider the effect of simple continuity
correction in the global central limit theorem for symmetric binomial distributions. Here, and in
higher-order Edgeworth approximation, we found optimal constants and asymptotically sharp
bounds on the approximation error. Furthermore, we prove asymptotically sharp bounds on the
error in the local case of a relative normal approximation to symmetric binomial distributions.
Additionally, we provide asymptotically sharp bounds on the approximation error in the local
central limit theorem for convolution powers of continuous and discrete uniform distributions.
Our methods include Fourier inversion formulae, explicit inequalities, and Edgeworth expansions, some of which may be of independent interest.
This thesis consists of four highly related chapters examining China’s rise in the aluminium industry. The first chapter addresses the conditions that allowed China, which first entered the market in the 1950s, to rise to world leadership in aluminium production. Although China was a latecomer, its re-entry into the market after the oil crises in the 1970s was a success and led to its ascent as the world’s largest aluminium producer by 2001. With an estimated production of 40.4 million tonnes in 2022, China represented almost 60% of the global output. Chapter 1 examines the factors underlying this success, such as the decline of international aluminium cartels, the introduction of innovative technology, the US granting China the MFN tariff status, Chinese-specific factors, and supportive government policies. Chapter 2 develops a mathematical model to analyze firms’ decisions in the short term. It examines how an incumbent with outdated technology and a new entrant with access to a new type of technology make strategic decisions, including the incumbent’s decision whether to deter entry, the production choice of firms, the optimal technology adoption rate of the newcomer, and cartel formation. Chapter 3 focuses on the adoption of new technology by firms upon market entry in four scenarios: firstly, a free market Cournot competition; secondly, a situation in which the government determines technology adoption rates; thirdly, a scenario in which the government controls both technology and production; and finally, a scenario where the government dictates technology adoption rates, production levels, and also the number of market participants. Chapter 4 applies the Spencer and Brander (1983) framework to examine strategic industrial policy. The model assumes that there are two exporting firms in two different countries that sell a product to a third country. We examine how the domestic firm is influenced by government intervention, such as the provision of a fixed-cost subsidy to improve its competitiveness relative to the foreign company. Chapter 4 initially investigates a scenario where only one government offers a fixed-cost subsidy, followed by an analysis of the case when both governments simultaneously provide financial help. Taken together, these chapters provide a comprehensive analysis of the strategic, technological, and political factors contributing to China’s leadership in the global aluminium industry.
Chapter 1: The Rise of China as a Latecomer in the Global Aluminium Industry
This chapter examines China’s remarkable transformation into a global leader in the aluminium industry, a sector in which the country accounted for approximately 58.9% of worldwide production in 2022. We examine how China, a latecomer to the aluminium industry that started off with labor-intensive technology in 1953, grew into the largest aluminium producer with some of the most advanced smelters in the world. This analysis identifies and discusses several opportunities that Chinese aluminium producers took advantage of. The first set of opportunities happened during the 1970s oil crises, which softened international competition and allowed China to acquire innovative smelting technology from Japan. The second set of opportunities started at about the same time when China opened its economy in 1978. The substantial demand for aluminium in China is influenced by both external and internal factors. Externally, the US granted China’s MFN tariff status in 1980 and China entered the World Trade Organization (WTO) in 2001. Both events contributed to a surge in Chinese aluminium consumption. Internally, China’s investment-led growth model boosted further its aluminium demand. Additional factors specific to China, such as low labor costs and the abundance of coal as an energy source, offer Chinese firms competitive advantages against international players. Furthermore, another window of opportunity is due to Chinese governmental policies, including phasing out old technology, providing subsidies, and gradually opening the economy to enhance domestic competition before expanding globally. By describing these elements, the study provides insights into the dynamic interplay of external circumstances and internal strategies that contributed to the success of the Chinese aluminium industry.
Chapter 2: Technological Change and Strategic Choices for Incumbent and New Entrant
This chapter introduces an oligopoly model that includes two actors: an incumbent and a potential entrant, that compete in the same market. We assume that two participants are located in different parts of the market: the incumbent is situated in area 1, whereas the potential entrant may venture into the other region, area 2. The incumbent exists in stage zero, where it can decide whether to deter the newcomer’s entry. A new type of technology exists in period one, when the newcomer may enter the market. In the short term, the incumbent is trapped with the outdated technology, while the new entrant may choose to partially or completely adopt the latest technology. Our results suggest the following: Firstly, the incumbent only tries to deter the new entrant if a condition for entry cost is met. Secondly, the new entrant is only interested in forming a cartel with the incumbent if a function of the ratio of the variable to new technology’s fixed-cost parameters is sufficiently high. Thirdly, if the newcomer asks to form a cartel, the incumbent will always accept this request. Finally, we can obtain the optimal new technology adoption rate for the newcomer.
Chapter 3: Technological Adoption and Welfare in Cournot Oligopoly
This study examines the difference between the optimal technology adoption rates chosen by firms in a homogeneous Cournot oligopoly and that preferred by a benevolent government upon firms’ market entry. To address the question of whether the technology choices of firms and government are similar, we analyze several different scenarios, which differ in the extent of government intervention in the market. Our results suggest a relationship between the number of firms in the market and the impact of government intervention on technology adoption rates. Especially in situations with a low number of firms that are interested in entering the market, greater government influence tends to lead to higher technology adoption rates of firms. Conversely, in scenarios with a higher number of firms and a government that lacks control over the number of market players, the technology adoption rate of firms will be highest when the government plays no role.
Chapter 4: International Technological Innovation and Industrial Strategies
Supporting domestic firms when they first enter the market may be seen as a favorable policy choice by governments around the world thanks to their ability to enhance the competitive advantage of domestic firms in non-cooperative competition against foreign enterprises (infant industry protection argument). This advantage may allow domestic firms to increase their market share and generate higher profits, thereby improving domestic welfare. This chapter utilizes the Spencer and Brander (1983) framework as a theoretical foundation to elucidate the effects of fixed-cost subsidies on firms’ production levels, technological innovations, and social welfare. The analysis examines two firms in different countries, each producing a homogeneous product that is sold in a third, separate country. We first examine the Cournot-Nash equilibrium in the absence of government intervention, followed by analyzing a scenario where just one government provides a financial subsidy for its domestic firm, and finally, we consider a situation where both governments simultaneously provide financial assistance for their respective firms. Our results suggest that governments aim to maximize social welfare by providing fixed-cost subsidies to their respective firms, finding themselves in a Chicken game scenario. Regarding technology innovation, subsidies lead to an increased technological adoption rate for recipient firms, regardless of whether one or both firms in a market receive support, compared to the situation without subsidies. The technology adoption rate of the recipient firm is higher than of its rival when only the recipient firm benefits from the fixed-cost subsidy. The lowest technology adoption rate of a firm occurs when the firm does not receive a fixed-cost subsidy, but its competitor does. Furthermore, global welfare will benefit the most in case when both exporting countries grant fixed-cost subsidies, and this welfare level is higher when only one country subsidizes than when no subsidies are provided by any country.
Today, almost every modern computing device is equipped with multicore processors capable of efficient concurrent and parallel execution of threads. This processor feature can be leveraged by concurrent programming, which is a challenge for software developers for two reasons: first, it introduces a paradigm shift that requires a new way of thinking. Second, it can lead to issues that are unique to concurrent programs due to the non-deterministic, interleaved execution of threads. Consequently, the debugging of concurrency and related performance issues is a rather difficult and often tedious task. Developers still lack on thread-aware programming tools that facilitate the understanding of concurrent programs. Ideally, these tools should be part of their daily working environment, which typically includes an Integrated Development Environment (IDE). In particular, the way source code is visually presented in traditional source-code editors does not convey much information on whether the source code is executed concurrently or in parallel in the first place.
With this dissertation, we pursue the main goal of facilitating and supporting the understanding and debugging of concurrent programs. To this end, we formulate and utilize a visualization paradigm that particularly includes the display of interactive glyph-based visualizations embedded in the source-code editor close to their corresponding artifacts (in-situ).
To facilitate the implementation of visualizations that comply with our paradigm as plugins for IDEs, we designed, implemented and evaluated a programming framework called CodeSparks. After presenting the design goals and the architecture of the framework, we demonstrate its versatility with a total of fourteen plugins realized by different developers using the CodeSparks framework (CodeSparks plugins). With focus group interviews, we empirically investigated how developers of the CodeSparks plugins experienced working with the framework. Based on the plugins, deliberate design decisions and the interview results, we discuss to what extent we achieved our design goals. We found that the framework is largely target programming-language independent and that it supports the development of plugins for a wide range of source-code-related tasks while hiding most of the details of the underlying plugin development API.
In addition, we applied our visualization paradigm to thread-related runtime data from concurrent programs to foster the awareness of source code being executed concurrently or in parallel. As a result, we developed and designed two in-situ thread visualizations, namely ThreadRadar and ThreadFork, with the latter building on the former. Both thread visualizations are based on a debugging approach, which combines statistical profiling, thread-aware runtime metrics, clustering of threads on the basis of these metrics, and finally interactive glyph-based in-situ visualizations. To address scalability issues of the ThreadRadar in terms of space required and the number of displayable thread clusters, we designed a revised thread visualization. This revision also involved the question of how many thread clusters k should be computed in the first place. To this end, we conducted experiments with the clustering of threads for artifacts from a corpus of concurrent Java programs that include real-world Java applications and concurrency bugs. We found that the maximum k on the one hand and the optimal k according to four cluster validation indices on the other hand rarely exceed three. However, occasionally thread clusterings with k > 3 are available and also optimal. Consequently, we revised both the clustering strategy and the visualization as parts of our debugging approach, which resulted in the ThreadFork visualization. Both in-situ thread visualizations, including their additional features that support the exploration of the thread data, are implemented in a tool called CodeSparks-JPT, i.e., as a CodeSparks plugin for IntelliJ IDEA.
With various empirical studies, including anecdotal usage scenarios, a usability test, web surveys, hands-on sessions, questionnaires and interviews, we investigated quality aspects of the in-situ thread visualizations and their corresponding tools. First, by a demonstration study, we illustrated the usefulness of the ThreadRadar visualization in investigating and fixing concurrency bugs and a performance bug. This was confirmed by a subsequent usability test and interview, which also provided formative feedback. Second, we investigated the interpretability and readability of the ThreadFork glyphs as well as the effectiveness of the ThreadFork visualization through anonymous web surveys. While we have found that the ThreadFork glyphs are correctly interpreted and readable, it remains unproven that the ThreadFork visualization effectively facilitates understanding the dynamic behavior of threads that concurrently executed portions of source code. Moreover, the overall usability of CodeSparks-JPT is perceived as "OK, but not acceptable" as the tool has issues with its learnability and memorability. However, all other usability aspects of CodeSparks-JPT that were examined are perceived as "above average" or "good".
Our work supports software-engineering researchers and practitioners in flexibly and swiftly developing novel glyph-based visualizations that are embedded in the source-code editor. Moreover, we provide in-situ thread visualizations that foster the awareness of source code being executed concurrently or in parallel. These in-situ thread visualizations can, for instance, be adapted, extended and used to analyze other use cases or to replicate the results. Through empirical studies, we have gradually shaped the design of the in-situ thread visualizations through data-driven decisions, and evaluated several quality aspects of the in-situ thread visualizations and the corresponding tools for their utility in understanding and debugging concurrent programs.
Differential equations yield solutions that necessarily contain a certain amount of regularity and are based on local interactions. There are various natural phenomena that are not well described by local models. An important class of models that describe long-range interactions are the so-called nonlocal models, which are the subject of this work.
The nonlocal operators considered here are integral operators with a finite range of interaction and the resulting models can be applied to anomalous diffusion, mechanics and multiscale problems.
While the range of applications is vast, the applicability of nonlocal models can face problems such as the high computational and algorithmic complexity of fundamental tasks. One of them is the assembly of finite element discretizations of truncated, nonlocal operators.
The first contribution of this thesis is therefore an openly accessible, documented Python code which allows to compute finite element approximations for nonlocal convection-diffusion problems with truncated interaction horizon.
Another difficulty in the solution of nonlocal problems is that the discrete systems may be ill-conditioned which complicates the application of iterative solvers. Thus, the second contribution of this work is the construction and study of a domain decomposition type solver that is inspired by substructuring methods for differential equations. The numerical results are based on the abstract framework of nonlocal subdivisions which is introduced here and which can serve as a guideline for general nonlocal domain decomposition methods.
Sowohl national als auch international wird die zunehmende Digitalisierung von Prozessen gefordert. Die Heterogenität und Komplexität der dabei entstehenden Systeme erschwert die Partizipation für reguläre Nutzergruppen, welche zum Beispiel kein Expertenwissen in der Programmierung oder einen informationstechnischen Hintergrund aufweisen. Als Beispiel seien hier Smart Contracts genannt, deren Programmierung komplex ist und bei denen etwaige Fehler unmittelbar mit monetärem Verlust durch die direkte Verknüpfung der darunterliegenden Kryptowährung verbunden sind. Die vorliegende Arbeit stellt ein alternatives Protokoll für cyber-physische Verträge vor, das sich besonders gut für die menschliche Interaktion eignet und auch von regulären Nutzergruppen verstanden werden kann. Hierbei liegt der Fokus auf der Transparenz der Übereinkünfte und es wird weder eine Blockchain noch eine darauf beruhende digitale Währung verwendet. Entsprechend kann das Vertragsmodell der Arbeit als nachvollziehbare Verknüpfung zwischen zwei Parteien verstanden werden, welches die unterschiedlichen Systeme sicher miteinander verbindet und so die Selbstorganisation fördert. Diese Verbindung kann entweder computergestützt automatisch ablaufen, oder auch manuell durchgeführt werden. Im Gegensatz zu Smart Contracts können somit Prozesse Stück für Stück digitalisiert werden. Die Übereinkünfte selbst können zur Kommunikation, aber auch für rechtlich bindende Verträge genutzt werden. Die Arbeit ordnet das neue Konzept in verwandte Strömungen wie Ricardian oder Smart Contracts ein und definiert Ziele für das Protokoll, welche in Form der Referenzimplementierung umgesetzt werden. Sowohl das Protokoll als auch die Implementierung werden im Detail beschrieben und durch eine Erweiterung der Anwendung ergänzt, welche es Nutzenden in Regionen ohne direkte Internetverbindung ermöglicht, an ebenjenen Verträgen teilnehmen zu können. Weiterhin betrachtet die Evaluation die rechtlichen Rahmenbedinungen, die Übertragung des Protokolls auf Smart Contracts und die Performanz der Implementierung.
Sozialunternehmen haben mindestens zwei Ziele: die Erfüllung ihrer sozialen bzw. ökologischen Mission und finanzielle Ziele. Zwischen diesen Zielen können Spannungen entstehen. Wenn sie sich in diesem Spannungsfeld wiederholt zugunsten der finanziellen Ziele entscheiden, kommt es zum Mission Drift. Die Priorisierung der finanziellen Ziele überlagert dabei die soziale Mission. Auch wenn das Phänomen in der Praxis mehrfach beobachtet und in Einzelfallanalysen beschrieben wurde, gibt es bislang wenig Forschung zu Mission Drift. Der Fokus der vorliegenden Arbeit liegt darauf, diese Forschungslücke zu schließen und eigene Erkenntnisse für die Auslöser und Treiber des Mission Drifts von Sozialunternehmen zu ermitteln. Ein Augenmerk liegt auf den verhaltensökonomischen Theorien und der Mixed-Gamble-Logik. Dieser Logik zufolge liegt bei Entscheidungen immer eine Gleichzeitigkeit von Gewinnen und Verlusten vor, sodass Entscheidungsträger die Furcht vor Verlusten gegenüber der Aussicht auf Gewinne abwägen müssen. Das Modell wird genutzt, um eine neue theoretische Betrachtungsweise auf die Abwägung zwischen sozialen und finanziellen Zielen bzw. Mission Drift zu erhalten. Mit einem Conjoint Experiment werden Daten über das Entscheidungsverhalten von Sozialunternehmern generiert. Im Zentrum steht die Abwägung zwischen sozialen und finanziellen Zielen in verschiedenen Szenarien (Krisen- und Wachstumssituationen). Mithilfe einer eigens erstellten Stichprobe von 1.222 Sozialunternehmen aus Deutschland, Österreich und der Schweiz wurden 187 Teilnehmende für die Studie gewonnen. Die Ergebnisse dieser Arbeit zeigen, dass eine Krisensituation Auslöser für Mission Drift von Sozialunternehmen sein kann, weil in diesem Szenario den finanziellen Zielen die größte Bedeutung zugemessen wird. Für eine Wachstumssituation konnten hingegen keine solche Belege gefunden werden. Hinzu kommen weitere Einflussfaktoren, welche die finanzielle Orientierung verstärken können, nämlich die Gründeridentitäten der Sozialunternehmer, eine hohe Innovativität der Unternehmen und bestimmte Stakeholder. Die Arbeit schließt mit einer ausführlichen Diskussion der Ergebnisse. Es werden Empfehlungen gegeben, wie Sozialunternehmen ihren Zielen bestmöglich treu bleiben können. Außerdem werden die Limitationen der Studie und Wege für zukünftige Forschung im Bereich Mission Drift aufgezeigt.