Geometrical Methods in Multivariate Risk Management: Algorithms and Applications

This thesis builds a framework for evaluating downside risk from multivariate data via a special class of risk measures (RM). The peculiarity of the analysis lies in getting rid of strong data distributional assumptions and in orientation towards the most critical data in risk management: those with asymmetries and heavy tails. At the same time, under typical assumptions, such as the ellipticity of the data probability distribution, the conformity with classical methods is shown. The constructed class of RM is a multivariate generalization of the coherent distortion RM, which possess valuable properties for a risk manager. The design of the framework is twofold. The first part contains new computational geometry methods for the high-dimensional data. The developed algorithms demonstrate computability of geometrical concepts used for constructing the RM. These concepts bring visuality and simplify interpretation of the RM. The second part develops models for applying the framework to actual problems. The spectrum of applications varies from robust portfolio selection up to broader spheres, such as stochastic conic optimization with risk constraints or supervised machine learning.

Economics of Ethical and Prosocial Behavior: Experiments on Social Responsibility, Ignorance, and Cheating

In this thesis I experimentally investigate prosocial and ethical behavior in economic interactions. The thesis consists of three experimental research papers that have a broad range of research questions on social responsibility, ignorance and cheating. With these experiments I aim to better understand when and why people behave ethically and/or prosocially and which consequences it has on their own and other players’ payoffs, and on overall efficiency. The results from the three experimental studies suggest that (i) donations to charity by employees are rewarded in an experimental setting, and the effect is driven by reciprocal concerns; (ii) there is a significant fraction of people who decide not to know about negative consequences of own actions, and the sorting of social agents of a low type into ignorance drives self-interested behavior of ignorant agents; and (iii) if the possibility of being exposed as a liar is small, the tendency to lie increases with incentives, indicating that some people have positive and finite costs of lying. Furthermore, when the participants lie, they lie to the full extent, which suggests that the intrinsic cost of lying is fixed.