The aim of this graduation work is theoretically describe and also demonstrate the practical application of the theory of credibility in the multidimensional case. This theory is one of the most frequently used methods for calculating premiums, expected claims frequency or the expected average amount of damage. In this work we describe multidimensional Bühlmann-Straub credibility model and two- dimensional model with a known distribution. For each of these models we derive credibility estimate and examples of using these estimates in practice. Both models are compared on simulated data. Powered by TCPDF (www.tcpdf.org)

In this thesis, we first go through classical results from the field of credibility theory. One of the most well-known models in the field is the Büuhlmann-Straub model. The model is relatively straightforward to apply in practice and is widely used. A major advantage of the model is its simplicity and intuitive dependency on its model parameters. From our perspective, the main drawback is the assumption regarding uncorrelated data. We show that the correlation can be used to cancel observational noise and therefore obtain more accurate estimators. This leads to an extended credibility formula that contains the Bühlmann-Straub model as a special case. This comes at the cost of introducing singularities which may cause the estimator to behave unexpectedly under certain circumstances. Further research is needed to better understand how often the circumstances are met in practice and if transforming the optimal weights could be a way forward in such cases. Finally, a simulation study based on real-world data shows that the proposed model outperforms the Bühlmann-Straub model.