The Underestimation of Risk Aggregates resulting from the Choice of Inadequate Semi-infinitely Supported Base Distributions and Correlation levels

The aim of the thesis is to analyze the underestimation of risk aggregations resulting from the choice of inadequate base distributions (single risk distributions) and correlation levels. The hypothesis of this thesis postulates that the choice of inadequate statistical single risk distributions and / or misconceptions regarding the interdependence of underlying single risks can - despite respective correspondence of the first and second central moments of the individual risks - result in significant underestimations of the overall risk specified by quantiles, hence coupled with unexpected substantial losses or costs. Additional consideration is given to the effects of different numbers of individual risks. Due to the practical relevance, the investigation primarily focuses on a selection of basic two-parametric distributions with semi-infinite support and, because of the complexity of the problem, on numerical simulation in conjunction with sensitivity analyses and the so-called Iman-Conover method. The analyses, results and recommendations of this thesis can be of particular relevance for practitioners and scientists in the fields of quantitative risk modeling and non-life insurance mathematics, not least in the context of expert elicitations.