This thesis deals with consumption-investment allocation problems with Epstein-Zin recursive utility, building upon the dualization procedure introduced by [Matoussi and Xing, 2018]. While their work exclusively focuses on truly recursive utility, we extend their procedure to include time-additive utility using results from general convex analysis. The dual problem is expressed in terms of a backward stochastic differential equation (BSDE), for which existence and uniqueness results are established. In this regard, we close a gap left open in previous works, by extending results restricted to specific subsets of parameters to cover all parameter constellations within our duality setting. Using duality theory, we analyze the utility loss of an investor with recursive preferences, that is, her difference in utility between acting suboptimally in a given market, compared to her best possible (optimal) consumption-investment behaviour. In particular, we derive universal power utility bounds, presenting a novel and tractable approximation of the investors’ optimal utility and her welfare loss associated to specific investment-consumption choices. To address quantitative shortcomings of those power utility bounds, we additionally introduce one-sided variational bounds that offer a more effective approximation for recursive utilities. The theoretical value of our power utility bounds is demonstrated through their application in a new existence and uniqueness result for the BSDE characterizing the dual problem. Moreover, we propose two approximation approaches for consumption-investment optimization problems with Epstein-Zin recursive preferences. The first approach directly formalizes the classical concept of least favorable completion, providing an analytic approximation fully characterized by a system of ordinary differential equations. In the special case of power utility, this approach can be interpreted as a variation of the well-known Campbell-Shiller approximation, improving some of its qualitative shortcomings with respect to state dependence of the resulting approximate strategies. The second approach introduces a PDE-iteration scheme, by reinterpreting artificial completion as a dynamic game, where the investor and a dual opponent interact until reaching an equilibrium that corresponds to an approximate solution of the investors optimization problem. Despite the need for additional approximations within each iteration, this scheme is shown to be quantitatively and qualitatively accurate. Moreover, it is capable of approximating high dimensional optimization problems, essentially avoiding the curse of dimensionality and providing analytical results.

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.

Based on data collected from two surveys conducted in Germany and Taiwan, my first paper (Chapter 2) examines the impact of culture through language priming (Chinese vs. German or English) on individuals’ price fairness perception and attitudes towards government intervention and economic policy involving inequality. We document large cross-language differences: in both surveys, subjects who were asked and answered in Chinese demonstrated significantly higher perceived price fairness in a free market mechanism than their counterparts who completed the survey in German or English language. They were also more inclined to accept a Pareto improvement policy which increases social and economic inequality. In the second survey, Chinese language induced also a lower readiness to accept government intervention in markets with price limits compared to English language. Since language functions as a cultural mindset prime, our findings imply that culture plays an important role in fairness perception and preferences regarding social and economic inequality. Chapter 3 of this work deals with patriotism priming. By conducting two online experimental studies conducted in Germany and China, we tested three different kinds of priming methods for constructive and blind patriotism respectively. Subjects were randomly distributed to one of three treatments motivated by previous studies in different countries: a constructive patriotism priming treatment, a blind patriotism priming treatment and a non-priming baseline. While the first experiment had a between-subject design, the second one enabled both a between-subject and within-subject comparison, since the level of patriotism of individuals was measured before and after priming respectively. The design of the second survey also enabled a comparison among the three priming methods for constructive and blind patriotism. The results showed that the tested methods, especially the national achievements as a priming mechanism, functioned well overall for constructive patriotism. Surprisingly, the priming for blind patriotism did not work in either Germany or China and the opposite results were observed. Discussion and implications for future studies are provided at the end of the chapter. Using data from the same studies as in Chapter 3, Chapter 4 examines the impact of patriotism on individuals’ fairness perception and preferences regarding inequality and on their attitudes toward economic policy involving inequality. Across surveys and countries, a positive and significant effect of blind patriotism on economic individualism was found. For China, we also found a significant relationship between blind patriotism and the agreement to unequal economic policy. In contrast to blind patriotism, we did not find an association of constructive patriotism to economic individualism and to attitudes toward economic policy involving inequality. Political and economic implications based on the results are discussed. The last chapter (Chapter 5) studies the self-serving bias (when an individual’s perception about fairness is biased by self-interest) in the context of price setting and profit distribution. By analyzing data from four surveys conducted in six countries, we found that the stated appropriate product price and the fair allocation of profit was significantly higher, when the outcome was favorable to oneself. This self-serving bias in price fairness perception, however, differed across countries significantly and was significantly higher in Germany, Taiwan and China than in Vietnam, Estonia and Japan. Although economic individualism and masculinity were found to have a significant negative effect on self-interest bias in price fairness judgment, they did not sufficiently explain the differences in self-interest bias between countries. Furthermore, we also observed an increase of self-interest bias in profit allocation over time in time-series data for one country (Germany) with data from 2011 to 2023. The four papers are all co-authored with Prof. Marc Oliver Rieger, and the first paper has been accepted for publications in Review of Behavioral Economics.

This thesis contains three parts that are all connected by their contribution to research about the effects of trading apps on investment behavior. The primary motivation for this study is to investigate the previously undetermined consequences and effects of trading apps, which are a new phenomenon in the broker market, on the investment and risk behavior of Neobroker users. Chapter 2 addresses the characteristics of a typical Neobroker user and a former Neobroker user and the impact of trading apps on the investment and risk behavior of their users. The results show that Neobroker users are significantly more risk tolerant than the general German population and are influenced by trading apps regarding their investment and risk behavior. Low trading fees and the low minimum investment amount are the main reasons for the use of trading apps. Investors who stop using trading apps mostly stop investing altogether. Another worrying result is that financial literacy among all groups is low and most Neobroker users have wrong conceptions about how trading apps earn money. In general, the financial literacy of all groups considered in this chapter is surprisingly low. The third chapter investigates the effects of trading apps on investment behavior over time and compares the investment and risk behavior of Neobroker users and general investors. By using representative data of German Neobroker users, who were surveyed repeatedly over a 8-month time interval, it becomes possible to determine causal effects of the use of trading apps over time. In total, the financial literacy of Neobroker users increases with the longer use of a trading app. A worrying result is that the risk tolerance of Neobroker users rises significantly over time. Male Neobroker users gain a higher annual return (non-risk-adjusted) than female Neobroker users. In comparison to general investors, Neobroker users are significantly younger, more risk tolerant, more likely to buy derivatives and gain a higher annual return (non-risk-adjusted). The fourth chapter analyses the impact of personality traits on the investment and risk behavior of Neobroker users. The results show that the BIG-5 personality traits have an impact on the investment behavior of Neobroker users. Two personality traits, openness and conscientiousness, stand out the most, as these two have explanatory power over various aspects of the behavior of Neobroker users. In particular, whether they buy different financial products than planned, the time they inform themselves about financial markets, the variety of financial products owned, and the reasons to use a Neobroker. Surprisingly, the risk tolerance of Neobroker users and the reasons to invest are not connected to any personal dimension. Whether a participant uses a trading app or a traditional broker to invest is respectively influenced by different personality traits.

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.