Optimal Approximation of Risk Scores Using the Infinity Norm

This thesis is concerned with how to approximate the risk score $y_i$ in risk management accurately using the infinity norm, since the approximation should also be explainable and interpretable for a mathematical layman. The idea behind this approximation is to automate the evaluation by using a linear model $y_i = a_0 + a_1 \cdot g_1(\pmb{x}) + a_2 \cdot g_2(\pmb{x}) + \dots + a_n \cdot g_n(\pmb{x}) + \epsilon_i$. The $g_j,~ j = 1,\dots, n$, denote the basis functions, which are obtained by using so-called fuzzy techniques, which are also described in this thesis, $\pmb{\epsilon}$ denotes the vector of error terms and $\pmb{x}$ is the input data. The coefficients $a_j$ have to be determined and at the same time their value indicates the importance of the respective basis function. Two different methods were considered for this purpose. One is the Remez algorithm, which provides relatively good approximations under certain conditions. However, this currently exists only for univariate functions, which is why it is also discussed which conditions would be necessary for the multivariate case. The other method uses a linear program. In this case, the maximum absolute error is minimized and the coefficients needed for the linear model are calculated by the constraints. The linear program gives good results considering the maximum absolute error. In the end there is also a short comparison of the results of the linear programming problem with the results when applying another norm.Tanja CobitMasterarbeit Universität Klagenfurt 202

Optimal Approximation of Risk Scores Using the Infinity Norm

This thesis is concerned with how to approximate the risk score $y_i$ in risk management accurately using the infinity norm, since the approximation should also be explainable and interpretable for a mathematical layman. The idea behind this approximation is to automate the evaluation by using a linear model $y_i = a_0 + a_1 \cdot g_1(\pmb{x}) + a_2 \cdot g_2(\pmb{x}) + \dots + a_n \cdot g_n(\pmb{x}) + \epsilon_i$. The $g_j,~ j = 1,\dots, n$, denote the basis functions, which are obtained by using so-called fuzzy techniques, which are also described in this thesis, $\pmb{\epsilon}$ denotes the vector of error terms and $\pmb{x}$ is the input data. The coefficients $a_j$ have to be determined and at the same time their value indicates the importance of the respective basis function. Two different methods were considered for this purpose. One is the Remez algorithm, which provides relatively good approximations under certain conditions. However, this currently exists only for univariate functions, which is why it is also discussed which conditions would be necessary for the multivariate case. The other method uses a linear program. In this case, the maximum absolute error is minimized and the coefficients needed for the linear model are calculated by the constraints. The linear program gives good results considering the maximum absolute error. In the end there is also a short comparison of the results of the linear programming problem with the results when applying another norm.Tanja CobitMasterarbeit Universit\ue4t Klagenfurt 202

Paper #151 Assessment of IT Governance

A shared view on the definition of IT governance is lacking and practitioners do not use present IT governance frameworks to support their decision-making. A commonly agreed upon definition of IT governance would be very useful and would serve the development and refinement of IT governance frameworks and assessment methodologies. This article presents an Architecture Theory Diagram, ATD, and a framework for defining IT governance based on an extensive literature study. IT governance is the preparation for, making of and implementation of IT-related decisions regarding goals, processes, people and technology on a tactical or strategic level. The framework for defining IT governance is eployed to compare how IT governance is defined in literature, and within a group of IT governance experts. Cobit is the most well-known framework for IT governance and it is frequently used by practitioners. While comparing Cobit’s definition of IT governance to the previously identified concerns of literature and practitioners, it showed that Cobit does support most needs, but lacks in providing information on how decisionmaking structures should be implemented. Background to Researc