Abstract
This thesis considers two main subjects divided in four problems in the broad field of mathematical finance. The first chapter treats option pricing followed by three chapters on the application of the machine learning algorithm of Random Forests to finance, specifically to risk capital aggregation, portfolio optimization and macro stress testing. In all four chapters new methodologies to treat the respective subjects are developed. All proposed models are benchmarked against commonly applied methods in the respective fields and found to outperform their peers.
Wälchli, Boris